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mf^^ \^x'i^<^ x^'O 




HARVARD UNIVERSITY. 



Bought 

with an appropriation nnade by 

the Corporation 

for books in Engineering. 



/deceived 



<IZ JI{aAxJu, l<fol. 



SCIENCE CENTER LIBRARY 



TRANSACTIONS 



OF 



t>iit imiiMm 0{ $«Kttt44P mA ^\iifMUtp 



IN SCOT LAN D 

(incorpobated). 



VOLUME XXVIII. 



TWENTY-EIGHTH SESSION, 
1884-85. 



EDITED BY THE SECRETARY. 



GLASGOW: 

PRINTED FOR THE INSTITUTION BY 

WILLIAM MUNRO, 80 GORDON STREET. 

1885. 



'^ l-iUC x; S 



iVIAR22 '^01 



OFFICE-BEARERS. 



TWENTY-EIGHTH SESSION, 1884-85. 



Presideiit 
Prof. JAMES THOMSON, C.E., LL.D., F.RS., Ac. 

Yioe-PreBidents. 
CHAS. C. LINDSAY, C.E. | liOBERT DUNCAN. 

T. ARTHUR ARROL. 



Goundllors. 



DAVID C. HAMILTON. 
CHARLES P. HOGG, C.E. 
PETER STEWART. 
ALEXANDER STEVEN. 
ROBERT DUNCAN. 



ROBERT DUNDAS, C.E. 
WILLIAM MACMILLAN. 
FRANK W. DICK. 
JAMES GILCHRIST. 
MATTHEW HOLMES. 



Finance Connnnittee. 

Prof. J. THOMSON, Convener. 
T. A. ARKOL. 
ALEXANDER STEVEN 
ROBERT DUNDAS. 



Library Connmittee. 

0. C. LINDSAY, CoNVKNKR. 
0. P. HOGG, 
PETKH STEWART. 
MATTHEW HOLMES. 



Honorary Treasurer. 
JAMES M. GALE, C.E., 23 Miller Street. 

Secretary and Editor of Transactions. 
W. J. MILLAR, C.E., 100 Wellington Street. 

Honorary Librarian. 
C. C. LINDSAY, C.E., 167 St. Vincent Street. 



Snb-Libraiian. 
THOMAS NAPIER, Institution Rooms, 207 Bath Street. 



CONTENTS. 



TWENT Y-P:IGHTH SESSION, 1884-85 



Office-Bearers, 



Page 
ill. 



PAPERS READ. 
Addreas by the President, Prof. James Thomson, C.E., LL.D., F.R.S., 
On Approximation to Curves of Stability from Data for Known Ships. 

(Discussion.) By Messrs F. P. Purvis and Kindermann, 
,, Manipulating the Material, and Building and Drilling the Great 
Tubes of the Forth Bridge. By Mr Andrew S. Biggart, C.E., . 
,, Energy and Entropy, and their Applications to the Theories of Air 

and Steam. By Mr Henry Dyer, C.E., M.A., . 

, , Mr Mansel's and the late Mr Froude's Methods of Analysing the 

the Results of Progressive Speed Trials. By Mr Wm. Denny, . 

Note on Tests of Turbines. By Professor R. H. Thurston, C.E., &c.. 

On Electrical Navigation, By Mr Allan Clark, 

„ A Continuous Regenerative Gas Kiln for Burning Fire-bricks, 

Pottery, &c. By Mr John Mayer, F.C.S., 
,, The Butt Fastenings of Iron Vessels. By Mr Staveley Taylor, . 
,, American Railway Freight Cai-s. By Mr Alexander Findlay, 
,, Sinking the Cylinders of the Tay Bridge by Pontoons. By Mr 
Andrew S. Biggart, C.E., . 



Minutes of Proceedings. 
Treasurer's Statement, 
Donations to Library, 
List of Members, . 
Index, 




15 

21 

35 

65 
199 
201 

207 
22T 
258 

263 

273 
284 
289 
293 
325 



PLATES. 
" Building and Drilling Tubes of Forth Bridge, . . I., II., III., IV., V. 

^ Analyses of Results of Progressive Speed Trials, VL, VII., VIII., IX., X., 

XL, XIL, XIIL, XIV., XV., XVL, XVII. 



'^ Electric Navigation, 
>- Continuous Regenerative Gas Kiln, 
y Butt Fastenings of Iron Vessels, . 
.. American Railway Freight Cars, . 



XVIlA. 

xvin. 

. XIX. 
XX., XXL 



' Sinking the Cylinders of the Tay Bridge by Pontoons, XXIL, XXIIL, XXIV. 



^toarb of ^ekl$ anb IPremmms of §oob 



FOR 



PAPERS READ DURING SESSION 1883-84. 



THE INSTITUTION MEDAL. 

To Mr Ralph Moore, C.E., for his Paper on 
** Cable Tramways.'' 



THE MARINE ENGINEERING MEDAL. 

To Mr John Harvard Biles, for his Paper on " The 
Stability of Ships at Launching." 



A PREMIUM OF BOOKS. 

To Mr Robert L. Weighton, M,A., for his Paper on 
"The Compound Engine Viewed in its Economical 
Aspect" 

A PREMIUM OF BOOKS. 

To Messrs Purvis and Kindermann for their Paper on 
" Approximations to Curves of Stability from Data for 
Known Ships." 



The responsibility of the statements and opinions given in the 
following Papers and Discussions rests with the individual authors ; 
the Institution, as a body, merely places them on record. 



INSTITUTION OF ENGINEERS & SHIPBUILDERS 

(INCORPORATED.) 



TWENTY-EIGHTH SESSION— 1 884-85. 

Introdtuioi-y Address, 
By Professor James Thomson, C.E., LL.D., F.R.S., President. 



Read 28th October, 1884. 



Gentlemen, 

In taking the Presidential chair at this first meeting of our 
new Session, I have to thank you for the honour you have done me 
in selecting me to be the President of this important Institution. 
I am fully sensible that honour of this kind involves also fluty and 
responsibility ; and I shall aim at doing my best to fulfil the trust 
you have placed in me. 

I think we are entitled to notice with satisfaction that our 
Institution continues to prosper. We have had, in recent years, a 
goodly array of valuable papers read at our meetings and published 
in our Transactions ; and the number of Members on our roll con- 
tinues to increase. 

I hope that, for the Session now opening, you will keep your 
minds duly impressed with the importance of providing good papers 
for our meetings. If each member will question himself as to what 
ideas, or results of experience, he has attained to, that may be new, 
and true, and useful for communication to his fellow-members ; and 

will, whether through generosity towards others, or for advance- 

1 



S The Presidetit's Address. 

mcnt of hifi own intoreets^ take the pains of bringing them before 
this Institution, in&fih that is deserving of development will be 
advanced in growth and fructification. 

It is customarily expected that a Presidential Address should be 
given at the commencement of each new Session. Accordingly, I 
propose now to offer a short address, having chosen not a wide 
range of subjects in engineering in general, but just two subjects, 
both of which I deem to be of real importance to engineers, and 
which commend themselves to me at present because they have 
engaged my own attention very much, and on them I think I have 
something useful to tell, or have useful considerations to adduce. 
The first of these will relate to considerations on the fundamental 
principles of the kinetic branch of dynamics— a subject which forms 
an essential part ki the science of mechanics. The second will 
relate to questions as to suitable means for attainment of safety, or 
for abatement of danger, in various kinds of engineering structures ; 
and my special purpose will be to show that the method by applica- 
tion of force-tests is deserving of more frequent and more consistent 
application than is customarily accorded to it. 

On the former of these subjects I have long felt the need of 
improvement in our modes of thought. We want more thoroughly 
clear fundamental ideas, and we want clear expressions in which to 
set them forth. Lately, I have been able, I think, to clear up some 
parts of this subject a little ; and I have, within the present year, 
submitted papers upon it to the Royal Society of Edinburgh, and 
my sayings to you this evening will include some passages from 
those papers. 

We are all accustomed to speak readily of the inertia of matter, 
though generally we would find it very diflicult to explain exactly 
what we mean by the term. No doubt we can understand that mani- 
festations of inertia are strikingly exhibited in the blows of a steam 
hammer, in the collisions of railway trains, and in those of ships at 
sea, and in the impacts of projectiles ; and we meet with it forcibly 
in the regulating eflfects of fly-wheels and governor balls. We are 



The Presidents Address* 3 

accustomed to overlook the deficiency of our knowledge of any 
explicitly clear principles on which the discrimination ought to 
depend of what shall constitute portions of time in the future equal 
to portions of time in the past ; while we cannot bring them to- 
gether to compare their lengths, as we might do with yard wands if 
we wanted to test their agreement. The past time has vanished 
already, and the future time has not yet come, and we cannot make 
the two be present together for comparison. 

One of our fundamental difficulties, then, relates to attainment of 
any principle for true chronometry, either in idea or in fact. 

The manifestations of inertia of matter are certainly connected 
with what is called changing motion ; but then we want clear ideas 
as to what may be any real distinction between changing motion, 
and either rest or changeless motion. 

In the universe of boundless and unmarked space we men have no 
means for knowing any condition to be called absolute rest. We 
do not know even how to imagine a distinction between rest and 
changeless motion. We have, however, through properties of 
matter, perfect means of distinguishing in principle between change- 
less motion and changing motion ; and, likewise through properties 
of matter, we have very good means of distinguishing practically 
among different degrees of rapidity of change of motion. 

The rocking of a cradle, the tossing of a ship on a stormy sea, the 
vibration of a pendulum or that of the balance wheel of a watch, 
and the continuous regular motion of a fly-wheel revolving uniformly, 
are all instances of changing motion, and are perfectly distinguish- 
able from the condition of changeless existence which, so far as we 
have any means of knowing, may be regarded as either rest or 
changeless motion. The last of the instances just named— that of 
uniform revolutional motion of a fly-wheel — might over hastily be 
mistaken for changeless motion; but the perpetual changing of 
direction of the motion of each small part of the rim of the fly-wheel, 
moving as it does in a circular path relatively to the ground, consti- 
tutes a perpetual changing of the motion. The statements just now 
made as to changing motion, such as may be felt by an infant in a 



4 The PreHdenfa Address. 

cradle, or by any person in the cabin of a ship tossed by wares, or 
such as belongs to any part of the rim of a fly-wheel revolving 
uniformly in a circular path relatively to the ground, may serve to 
introduce some preliminary notions as to there being truly in nature 
modes of existence of matter which may be designated intelligibly 
as changing motion. 

At first sight many of us might fancy that we understand quite 
readily the reciprocating motion of the bob of a pendulum going 
forward and backward in its circular arc within the clock case. 
Let us, however, introduce further the thought of the earth shooting 
forward in its annual orbit round the sun, with a velocity of about 
18 miles per second, and carrying the clock case and clock with it, 
while the pendulum may be moving relatively to the case at 
quickest perhaps only with a velocity of a few inches per second ; 
and the nature of the changes of motion in progress, whether as to 
velocity or direction, will not be very evident, and may indeed 
become rather perplexing to the mind. 

After the announcement which has been made of our utter 
inability to know of any condition to be called absolute rest in a 
boundless and unmarked universe, anc} the suggestion put forward 
of perplexities or more than perplexities as to direction of motion in 
the universe, and the concomitant assertion on the other hand that 
there is truly in nature a condition to be called change of motion 
which can be practically appreciated by men; it may be some 
comfort to be told of a most important truth discovered in the 
nature of things— the truth that there is a real distinction, appreci- 
able with extremely great exactitude to men, between rotational rest 
and rotational motion in the unmarked universe. 

During by far the greater part of the period within which men 
have given any attention to astronomical and other physical questions, 
the earth has been very generally supposed to be at rest, and the 
sun, moou; and stars have been supposed to revolve round the earth, 
most of the stars appearing as if fixed together in the heavens, and 
as if revolving together in a period slightly shorter than that of the 
solar day. It was thus supposed that straight lines directed from 



The Presidenfa Address. 5 

as towards the stars — such, for iostanoe, as the straight lines along 
which we look in viewing the stars— are not directionally at rest in 
the universe; but that each of them participates in the supposed 
revolution of the star towards which it is directed, and has direc- 
tional or rotational motion in sweeping out angular space round our 
own station on the earth as a vertex. Directional fixity was 
assumed to belong to straight lines attached in unchanging configura- 
tion to the earth imagined itself as being at rest. 

Belief to the effect so described was prevalent, and was very 
dominant in past times, down to the period of Oalileo, about 300 
years ago. In those former times there was no physical principle, 
nor any valid reason known to men, which could afford a criterion 
for deciding on any particular condition as being one of absolute 
rotational rest in the universe. It is now, however, discovered and 
fully established that there is a real and true principle in nature 
determining a condition of absolute rotational rest. It is also fully 
established that lines of direction almost perfectly unchanging are 
available to us in the straight lines from the stars designated as 
*^ fixed stars*' to any observer's station on the earth. 

Out of multitudinous considerations founded mainly on astrono- 
mical observations — the nature of some of which may be suggested 
by the remarks just made^there have emerged to the notice, and 
to the more or less clear cognisance of men, a few profoundly im- 
portant dynamic laws which have come to form the basis for further 
dynamic reasonings, and, to us engineers, the basis for most of our 
investigations in mechanics. 

Sir Isaac Newton sets forth, under the designation of the First 
Law of Motion, the statement thtiir-Eveiy body continues in its 
slate of resting or of moving uniformly in a straight course, except in so 
much as by applied forces it is compelled to change thai state. 

A most important truth in the nature of things, perceived with 
more or less clearness, is at the root of this enunciation ; but the 
words, whether taken by themselves, or in connection with Newton's 
prefatory and accompanying definitions and illustrations, are inade- 



6 The PresiderU's Address. 

qaate to give ezpresBion to that great natural truth. In attempting 
to draw from the statement a perfectly intelligible conception, we 
fiad ourselves confronted with the preliminary difficulty or impossi- 
bility as to forming any perfectly distinct notion of a meaning in 
respect to a single body, for the phrase " state of resting or of moving 
uniformly in a straight course" Newton's previous assertion thai there 
exists absolute space which, in its own nature, without reference to anything 
else^ always remains dtUce and immovable, does not clear away the 
difficulty. It does not do so, because it involves in itself the whole 
difficulty of our inability to form a distinct notion of identical points 
or places in unmarked space at successive times, or of our iuabiiity 
to conceive any meaus whatever of recogaizing afterwards in any 
one point of space, rather than in any other, the point of space 
which, at a particular moment of past time, whb occupied by a 
specified point of a known body. We have besides, as I have 
already mentioned, no preliminary knowledge of any principle of 
chronometry; and, for this additional reason, we are under an 
essential preliminary difficulty as to attaching any clear meaning 
to the phrase state of moving uniformly in a straight course^ the uni- 
formity being that of equality of spaces passed over in equal times. 
The only motion of a point that men can know of, or can deal 
with, is motion relative to one, two, three, or more other points. 
Three points marked or indicated on one, two, or three bodies, the 
centres, for instance, of three balls, whether preserving their distances 
apart, unchanging or not, are sufficient for enabling us to construct 
or to imagine a reference frame of any changeless configuration 
desired — three rectangular co-ordinate axes, for instance, or three 
rectangular co-ordinate planes — to which the situations, instantaneous 
or successive, of points may be referred. We may have a firm per 
suasion, even without perfect understanding, that, in the nature of 
things, there must be a reality corresponding to our glimmering 
idea of motion of a body along a straight course with changeless 
velocity ; and that there must be an essential distinction between 
such motion and motion along a curved course, or motion with 
varying velocity. We cannot, however, specify such motions 



The Presidtnfs Address, \ 

relatively to unmarked space and unmeasured passage of time. 
Briefly, we can deal only with relative motions or relative rest ; 
not with absolute motions nor absolute rest. 

Sir Isaac Newton sets forth as the Second Law of Motion in his 
arrangement, a statement to the effect : — 

That, Change of motion is p'oportional to the magnitttde and duratum 
of tiie applied force, and takes place in tfie direction in which that force 
is applied. 

His Thikd Law is to the eflFect :— 

That, AcHcn is alicays accompahied by equal and opposite re'aciiq;n ; 
or the mutual actions of two bodies^ each on the other^ are equal and 
opposite. 

It may now readily be noticed, that Newton's enunciation, set 
forth as the Second Law, involves elements of obscurity alike with 
that which has been shown already as rendering the enunciation of 
the first law inadequate for expreesing the great natural truth to 
which it relates. 

I will now proceed briefly and without trespassing on your 
patience by attempting to enter into any elaborate illustrations, tc 
mention an amended mode of enunciating what men really can 
know in respect to the natural law or laws here referred to. 

Let us introduce the conception of a reference frame to which the 
situations and motions of any moving points" are to be referred, and 
let us introduce also the conception of what may be called a dial 
traveller, consisting of a hand, like that of a clock, travelling round 
a dial ; the motion being produced in any way so as to accomplish 
conditions to be afterwards specified. 

Now, we are to accept as an established law of nature, established 
through multitudinous observations and speculations, together with 
theories confirmed by multitudinous agreements, the following, 
which may be called the Law of Inertia. 

THE LAW of inertia. 

For any set of bodies, acted on each by any force, a reference 
FRAME and REFERENCE DIAL-TRAVELLER are kinematically possible, 



8 The Prebideni's Address. 

such that relatively to them conjointly, the motion of the mass- 
centre of each body, undergoes change simultaneously with any 
infinitely short element of the dial traveller progress, or with any 
element during which the force on the body does not alter in 
direction nor in magnitude, which change is proportional to the 
intensity of the force acting on that body, and to the simultaneous 
progress of the dial-traveller, and is made in the direction of the 
force. 

From this Law of Inertia the Principle of Chronometry is readily 
deducible, as a corollary, by elementary mathematical considerations, 
and it may be enunciated thus : — 

Any dial-traveller, which would accomplish the conditions stated, 
would make progress proportionally with any other dial-traveller, 
obtained likewise from the same set of bodies, or any other set of 
bodies with the same or any other reference frame. Then, in view 
of this remarkable agreement, we define as being equal intervals of 
time, or we assume as being somehow in their own nature intrin- 
sically and necessarily equal intervals of time, the intervals during 
which any such dial-travoUer passes over equal spaces on its dial. 
Thus, any dial-traveller which would accomplish the conditions 
stated, would constitute a perfect chronometer. 

This gives us the ideal of a perfect chronometer. It remains for 
men to aim at approaching as near as they can towards that ideal 
in the practical realization of good chronometry. 

For good and long-enduring raelizations of chronometry, astrono- 
mical methods are alone available. None of these present any 
simple method of procedure. They require hypothetical assumptions 
of supposed forces acting on the bodies considered, and, above all, 
there is involved in them the assumption, and after multitudinous 
tests, accompanied by multitudinous confirmations, the discovery of 
the Law of Universal Gravitational Attraction — the grandest of the 
discoveries of Sir Isaac Newton. 

Further the principle of Absolute Directional or Rotational Rest, 
and of Absolute Rotation is also readily deducible, and may be 
stated thus : — 



The Prmdents Address. 9 

Any sfcraight line fixed relatively to any reference frame which 
accomplishes the conditions specified in the statement of the Law of 
Inertia, has absolute rotational or directional rest. If another 
straight line fixed in any other such reference frame be parallel to 
that former line, the two lines will continue parallel, so that by 
either of them the one same absolute direction is permanently 
preserved. 

The principle here called that of absolute directional rest is 
clearly enunciated in Thomson and Tait's Natural Philosophy^ § 249, 
under the designation of " Directional Fixedness." It is there 
exhibited by a very simple device, from, which, however, that just 
now stated is difierent. 

Any body which has no rotation relative to a framing, which 
accomplishes the conditions stated, is devoid of absolute rotation. 

The Law of Inertia, here enunciated, sets forth all the truth 
which is either explicitly stated or is suggested by the first and 
second laws in Sir Isaac Newton's arrangement ; and by a slight 
extension of collateral explanations, it can be made to include also 
the truth that is in the third law. 

By applying the Law of Inertia to the case in which the forces 
acting on the bodies vanish, the law becomes a remodelled sub- 
stitute for the statement set forth by Sir Isaac Newton as the First 
Law of Motion in his arrangement. 

Now, gentlemen, I have to say, and I think you will agree with 
me in the opinion, that some of the considerations I have been 
bringing before you have been rather abstruse, and have been not 
quite easy for complete comprehension on their first presentation. 
I will try, however, to make amends now by offering to you one or 
two cases in illustration, which, I think, are very easily understood 
and easily carried in the mind. 

It is told of the great Syracusan philosopher of old, that he said 
'' Give me a fulcrum and I will move the world." But another 
great philosopher — one who has been contemporary with ourselves, 
the late Professor Clerk Maxwell — has taught us how to perform 



10 Tke PreMefivts Address. 

the more wonderful feat of changing the earth's motion and leaving 
it permanently altered, without our having to seek for aid from any 
external fulcrum or anything external to the earth itself. To do 
this, all that is required will be accomplished if we look towards the 
pole-star, and wave the hand with a motion of revolution round the 
line of vision so assumed. In other words, the deed will be done if 
we make any wheel or any mass of matter revolve in a plane 
parallel to the earth's equatorial plane. While the mass is revolving 
the speed of the earth's diurnal revolution is different from what it 
would be if the mass were left standing stilL llie effect of the 
operation thus performed would be, I must admit, very small 
indeed ; but engineers, when once they know of something that can 
be done, even in a very small way, are generally eager V> carry it 
out on a larger scale. Great operations on the earth do not deter 
them, if only a company can be formed and the money be amply 
provided. Let them then construct a Grand Equatorial Belt 
Bailway round the earth, and set heavily loaded trains on it ; and, 
if they want to lengthen our days, let them run the trains forward 
from west to east The earth will now be revolving slower than 
before; and if, at any time after several months or years have 
passed, the trains be all stopped, the earth will revert to its old 
speed of revolution; but it will then, at any instant of time 
(indicated, it may be, astronomically, by an eclipse of a satellite of 
Jupiter, for instance), be behind the position of diurnal revolution, 
which it would have had if the trains on that great railway line 
had not been in motion. 

To proceed now to another case : — Let us suppose that a cannon 
is placed at the North Pole, and is fired towards a vertical flagstaff 
standing at a distance of 4 miles from the Pole. Let us suppose that, 
at the instant when the ball is leaving the gun, a certain star is just 
behind the flagstaff so as to be hidden from the gunner when taking 
aim. Let the ball be supposed to move at 1960 feet per second as 
the horizontal component of its velocity ; and, for simplicity, let it 
be supposed that this velocity will be maintained throughout the 
flight. On the supposition of the motion being unaffected by 



The Presidenfa Address. 1 1 

resistance or disturbance from tfae air, let us entertain the question: 
— How ufill the ball fly as to the horizontal projection of its path over the 
earth f A little consideration and calculation will bring out the 
answer to be this : — ^The ball will fly in a vertical plane passing, at 
the first instant of the flight, through the earth's axis, and the flag- 
staff^ and the distant star. This vertical plane of the ball's motion 
will continue to be directed from the earth's asds out towards the 
star, but the flagstaff will be moving away from that plane to the 
eastward with the rotation of the earth ; and the flagstaff, at the 
moment of the ball's passing it, will have escaped to the east by a 
distance of 16^ feet from the course of the ball 

If, further, we raise the question as to how the projectile would 
proceed out through space, as shot from the gun towards the distant 
star ; and if, for simplicity, we imagine it to be unaffected by the 
earth's attraction, or by any force whatever; and if we suppose the 
gunner^s aim to have been perfect, so that the ball in departing 
continues to eclipse the star from his eye ; we shall have to conclude 
that the ball, in its straight course with changeless velocity through 
space, may be going along any straight line whatever, quite as well 
as going along that one which would take it ultimately into collision 
-with the star. This statement looks puzzling ; but to bring out the 
truth more clearly, let us imagine a reference frame founded on two 
or more straight lines extending out from the distant star, and both 
or all of them maintaining absolute directional rest, or non-rotation. 
We may now understand that the earth, and with it the gun, will 
very surely be moving, relatively to that frame, in some direction 
utterly unknown to us, and with some velocity quite as unknown as 
the direction, while the velocity may even be vastly great in com- 
parison to the velocity of departure of the ball from the gun. Thus 
it may even be the fact that the ball, in proceeding through space, 
may, so far as we can tell, almost as likely be increasing its distance 
from the star, as getting nearer to it ; and, relatively to the reference 
frame attached to the star as ahready explained, the ball's straight 
course may be in any direction whatever. 



12 The Presidenfs Address. 

I have now finiahed all that I would propose on this occasion to 
lay before you on the Laws of Motion, and the Law of Inertia and 
Principle of Ghronometry. I aimed at being very brief, but in spite 
of my efforts, the subject compelled me to expand ; and there is left 
now very little time reasonably available for the second of my 
intended subjects for this address. 

I will now proceed, however, to make a few remarks in advocacy 
of more frequent and more consistent applications of force-tests than 
is customarily accorded to them, for the attainment of safety or 
abatement of danger in various kinds of engineering structures. I 
have already included this subject in an introductory lecture delivered 
in the University of Glasgow on the occasion of my first entry on 
my professorship there, and that lecture was soon after published. 
There may therefore not be much reason for my renewing at any 
considerable length on this occasion the arguments there put forward; 
and I think it best at present to do little more than to offer a very 
few recommendations and suggestions. 

In many of the materials and structures, on the sufficiency of 
which in respect to strength, human life is staked, there may exist, 
through various modes of origin, unseen flaws or imperfections. 
There may also be faults of design, in some cases, as to which the 
best available science applied through methods of calculation may be 
practically inadequate for their avoidance. In many such cases where 
force-tests are not applied at all, or if applied, are not severe enough 
or not often enough renewed, faults or imperfections may pass 
unnoticed which might be brought to light by such a test as would 
do no harm to the structure if free from the defect or flaw in the 
material or in the design. 

In respect to boilers as commonly used on land, I do not think 
there is any established system, or prevalent usage, for ascertaining 
their sufficiency, in respect to strength, better than the system 
practised under the Board of Trade for the boilers of steam ships 
carrying passengers. Now in the Board of Trade's instructions to 



The FreMefU'8 Address. 13 

their surveyors, while it is made a rule that surveyors should see all 
new boilers, and boilers that have been taken out of the ship for a 
thorough repair, tested by hydraulic pressure up to at least double 
the working pressure that will be allowed, which allowance for 
working pressure is intended to be arrived at from inspections'and 
measurements through calculations under prescribed rules and 
formulas, and not by the hydraulic test. It is also] stated Jthat [in 
the case of old boilers care is to be taken, in testing, not to overstrain 
them, but that the test mmt always exceed the working pressure. 

Thus, while for new or thoroughly repaired boilers, there is pro- 
vision for a proved or ascertained strength, double of that inten- 
tionally allowed to be brought into play in ordinary work, yet in 
the case of old boilers, which may have undergone much corrosion 
and damaging usage in many ways, there appears to be no provision 
for any definite amount of proved excess of strength beyond that 
called into exertion in ordinary work under the allowed working 
pressure. But instead of the provision of any, even small, specified 
margin for safety, there is a caution given that care mtist be taken not 
to overtrain Ae boikr, coupled with the instruction that the test 
pressure must always exceed the working pressure. The tendency of 
this instruction on the mind of a careful and submissive inspector — 
submissive to the instructions of the higher authorities — ^must 
naturally be to make him, when a boiler appears rather critical and 
of dubious safety, tend to subject it to scarcely any excess of 
pressure beyond the sanctioned working allowance. Now, I do not 
think this is a desirable state of things. It appears to me that the 
best formulas and other means for calculating, estimating, and guess- 
ing the capabilities of endurance of a boiler, can bear no comparison 
with tfie hydraulic test as to trustworthiness. Strong confirmation 
of this opinion, it appears to me, can be drawn from an instruction 
given by the Board themselves, in their paragraph 73, vi«., 
''Strength of Boilers to he Ascertained^ and Working Pressure fixed by 
Caleulation. — Before testing a boiler, the Surveyor should examine 
it, take the necessary measurements, and calculate what the working 
pressure should be, in accordance with the Board of Trade Segula- 



14 The Fresidmfs Address. 

tions, and only test to double the working pressore ; if the test is 
not Batisfactory, the defects must be made good, and the boiler 
re-tested" 

It seems to me that the idea pat forward in the title of this 
instruction is rather different from that which is virtually brought 
out in the instruction itself. The title says that the strength of 
the boiler is to be ascertained, and the working pressure to be 
fixed, by calculation ; but the instruction ordains that when the 
formulas, rules, and calculations have all been found in a particular 
case to hare been in vain, and to have been fallacious guides for 
ascertainment of the actual strength of the boiler, that boiler is to 
be somehow altered, or amended, so as to increase its strength, until 
it can exhibit by the hydraulic test, not a vainly calculated strength, 
but a proved strength coming up to a previously calculated but 
practically unattained standard. Here it is certainly the force-test, 
not the formulated calculation or estimate, that is the final arbiter 
for deciding how the boiler may be worked. 

The subject now touched upon would, if it were to be properly 
treated, open out to an indefinitely wide extent. Time would not 
now permit, and the present occasion would not be suitable, for 
entering into it with anything like the fulness that it deserves. I 
will only say further that I hope that in some of our future meetings 
in the Session now opening, the discussion of the subject through a 
much wider range of practical cases may be taken up by various 
members of our Institution. 



On Apprmmatian to Curves of Stability, from Data for Known Ships. 
By Messrs F. P. Purvis and B. Kindsrmann. 



The discussion of this paper, which was held as read on the 22nd 
April, 1884, took place on the 28th October, 1884. 

On the suggestion of the President^ 

Mr Purvis gave a short resume of the paper. In speaking of the 
curves appended, he described them as forming the chief value of 
the paper, and not simply illustrations. In starting on the consider- 
ation of the matter of approximation, they had set before them the 
determining in an approximate manner of some means by which to 
arrive at a knowledge of the stability of a vessel without having the 
labour of making the calculations involved in any known method — 
they wanted to discover some basis on which a satisfactory approxi- 
mation could be founded, and in doing so they kept before their 
minds three primary considerations as affecting stability — ^viz., the 
dimensions of the vessel, its form, and the height of its centre of 
gravity. The latter was outside the scope of any rule ; but they 
were able to take up the question of the dimensions, reserving that 
of form to be treated of afterwards, either by themselves or others. 
For a vessel of the type to which the curves had reference, the 
' means of determining the stability was provided, whatever the 
dimensions. They claimed that these curves gave^ not an approxi- 
mation only to the stability, but the absolute stability itself, and 
any one looking into them would see that this was the case, if only 
the vessel dealt with were of the type form. The original ship 
might be considered as an elastic body, which could be drawn out 
or contracted in any one of the three directions — ^length, breadth, 
and depth — and for any ship so produced, the curves gave the 
righting arms absolutely for angles of 15, 30, 45, 60, 75, and 
90 degree% and for a position of centre of gravity coincident 



16 On Approximation io Curves of StabilUy, 

with the metacentre. What they had thus done, was to cover 
the ground for one type of ship only; they wanted next to see 
results that would be applicable to a ship of any type. In the 
practical use of the curves given for approximating purposes, two 
difficulties would be sure to arise. First of all, the sheer of the 
new ship would probably not be the same as that of the type ship, 
and as the sheer has considerable effect at large angles of heel, abso- 
lute trustworthiness could not be obtained. They had attempted 
to lay down guiding principles to overcome this difficulty. A more 
important difference would arise if, having the dimensions of a certain 
vessel, and making use of the curves on Plate XYII. (seeYoLXXYII.) 
to obtain the height of the metacentre, the user were to find that the 
height of the metacentre thus obtained was much different from 
that of the metacentre of the actual vessel. This point Mr Purvis 
illustrated on the blackboard, and showed that the assumption 
which would probably give the best result was that the righting 
arms given by the curves were for a position of centre of gravity 
identical with the metacentre of the actual ship, and not with the 
metacentre of the type ship. 

Mr Robert Mansel said that the problem to the solution of 
which Messrs Purvis and Kindermann had addressed themselves, 
was one of great difficulty, which had been attempted to be solved 
in many ways; and, doubtless, each of them, to its inventor, 
appeared the simplest and best For his own part, he should not 
like to place confidence in any generalized approximation, unless it 
were checked by direct calculations on the actual vessel in question. 
It was praiseworthy in Messrs Purvis and Kindermann to inves- 
tigate the question, so as to see how far it was possible to approxi- 
mate with type ships of the same geometrical form but different 
dimensions; if guarded against the error of assuming that the centre 
of gravity of each respective vessel was in the same relative position. 
Many years ago,* he had gone some way into the system of applying 
the calculated abstract ratios of type ships to others of different 

* See ''Seotdsh Shipbuilders' Transactions,*' October, 1861. 



ftum Dotafor Known Ships. 17 

dimensions, but he had not attempted to cany it so far as now 
proposed, to the comparison of stabilities. The real difficulty lay in 
the determination of the exact position of the centre of gravity of 
the hull and its lading ; the above, and other recently proposed 
systems, dealt with the variations of the centre of buoyancy, to the 
neglect of the equally involved and necessary variations of the height 
of the centre of gravity, as stated in the following quotation from 
the above-noted paper : " The complete investigation of the stability 
of floating bodies, upon strict mechanical principles, has been pub- 
lished a few years ago by Canon Moseley, who properly named the 
object of his investigation the dynamical stability of those bodies. 
Thus, instead of considering the moment of restoration when tho 
vessel is deflected through the given angle, Canon Moseley proposes 
to calculate the work which must be done during the motion from 
the upright to the deflected position. Obviously, the more work 
done in deflecting the vessel through a given angle, the greater is 
her stability. Now, to do work upon the vessel, we must raise her 
centre of gravity, or depress her centre of buoyancy j but, in the 
deflection, we may find that the centre of gravity sinks, or the centre 
of buoyancy rises. In either case, the corresponding work is an- 
tagonistic to the stability, and must be subtracted from the work to 
be done. Hence, considering the variation of the height of the 
centres positive when they go to increase the stability, and negative 
when they tend to diminish it, then the algebraic sum of the varia- 
tions of height of the centres of gravity and buoyancy, in moving 
from the upright to the deflected position, multiplied by the weight 
of the vessel, is the measure of the dynamical stability of that vessel. 
In addition to this, in all ordinary cases, in the act of heeling we 
will have water displaced and moved aside. The work involved in 
this motion goes to increase the dynamical stability, and ought to 
be included in a strict investigation, but would be much more diffi- 
cult and uncertain to calculate than even the position of the centre 
of gravity. . . . One deduction of theory, confirmed by experi- 
ment, however, is worthy of notice. It is this : a pressure, such as 
a sudden and' constant gust of wind, will deflect a vessel through 



18 On Apprfodmation to Curves ofSktlnliiy, 

twice the angle at which the same presfiure would keep]]^the vessel 
permanently deflected." 

Mr J. Macfarlane Gray, of the Board of Trade, London, as a 
stranger asked permission to say a few words. He was afraid, in 
reference to whaf^Mr Mansel had said, that that gentleman's remarks 
might convey an erroneous impression. There could be no question 
that as regards absolute trustworthiness, that the tables given being 
accurate for the type ship, must also be accurate for similar vessels, 
which could be derived from the type ship by either lengthening or 
shortening, or crushing or expanding it sideways, so that any one 
using those tables to get the stability of a vessel of the same type 
was in reality going to the actual vessel itself — the very thing Mr 
Mansel said he preferred to do — without instituting special calcula- 
tions, or doing the work himself. He was of opinion that what was 
wanted was to get the stability of a vessel with the same ease and 
accuracy as at present they could work a problem in trigonometry, 
by merely turning up a table, get the values of sines and tangents. 
He thought they all must be very much indebted to Messrs Denny's 
staff for having brought that paper before the Institution. 

Mr Purvis said he had to thank Mr Gray for his remarks, which 
quite answered Mr ManseFs objection. The question o! the varia- 
tion of type Mr Biles had touched upon in his paper last session, 
giving curves of stability for different vessels of the same dimensions, 
and at one particular draught ; one vessel especially a very fine and 
another a very full one. What Mr Biles had done for one draught 
he would like to see carried through all variations of draught. Of 
course, that would involve a great deal of work. He looked upon 
the present paper, laborious as it had been, as merely introductory 
to the subject, and he trusted they would yet make further investi- 
gations on the effect of a variation of the types. 

Mr J. Macfarlane Gray remarked that he might have said 
when on his feet that the method of types is not absolutely novel, 
for he had found recently the germ of the same treatment of this 
subject in an ancient book. Archimedes carried out the same inves- 
tigation 2100 years ago, in what is substantially the very same way 



from Data for Known Shij>s, 1 9 

as Messrs Purvis and Kindermann had done now. It appeared that 
he had worked out with perfectly mathematical accuracy the problem 
for parabolic conoids of all proportions, and that he had formed 
rules for comparing the stability of those, and that the ships at 
that period, so far as the question of stability, might be validly 
treated as of this parabolic form. He (Mr Gray) explained that if 
these conoids were extended lengthwise, made say twelve times 
longer, retaining each section as before, they would get a figure 
which would not be unlike the vessels of the ancients; so that 
Archimedes might be said to have investigated the problem of the 
stability of ships of his time substantially as the authors of this 
paper were doing now — and there is nothing new under the sun. 
The merit of origination was still due to the authors of the .paper, 
and when he pointed out that in what they had done they had been 
working alongside of Archimedes, Messrs Purvis and Kindermann 
would not object to the companionship. 

The President said that he was sure the efforts of Messrs 
Purvis and Kindermann to bring out new methods intended to save 
labour, and to render information more readily available, deserved 
their praise and thanks. He trusted they were ready to give a 
warm vote of thanks to these gentlemen. 

The voti^ was unanimously agreed to. 



On Mampdaling the Material, and Buildingj and Drilling the Great 
lubes of the FoHh Bridge. 

By Mr Andrew S. Biggart. 



(SEE PJATES I., II., III., IV., AND V.) 



Received 22nd; Read 25th November', 1884. 



The Forth Bridge has on various occasions formed a theme of 
deservedly widespread interest, and the general character of the 
undertaking, is more or less familiar to engineers. A comprehensive 
view of the subject, and of the numerous engineering questions 
involved, has also been lately so ably given by Mr Baker, that the 
writer purposes in this paper to at once pass on to examine some of 
the later details of the manufacture of the superstructure ; such as, 
that of the work in connection with the great tubes. 

One of the well-known features in the design of this undertak- 
ing demands that struts of hitherto unequalled length, and 
capabilities for resisting thrust, be employed. The form which best 
fulfils these conditions is the tubular. 

As well nigh six miles of tubes are required in the completed 
Bridge, it at once becomes evident that the construction of them 
could only be effected within a reasonable time, by the adoption of 
special plant. Owing also to their novelty of form and great size, 
no machinery was in existence capable of dealing with such work. 
On account of this, and for various other reasons, Mr Arrol 
determined to design special plant for the whole work, the descrip- 
tion of a part of which, and the mode of working the same, can be 
but scantily treated of in this paper. 



22 On the Forth Bridge. 

The struts required are of various dimensions, ranging from that 
of the largest, which is 12 feet diameter, to that of the smallest, 
which is only 3 feet. The description of the former will be con- 
sidered in this paper, although all are very much alike in design. 

Fig. 1, Plate II., shows the cross section of one of the 12 feet 
horizontal tubes between the piers. It consists of 10 plates and 10 
longitudinal H beams, stiffened at intervals of 8 feet by means of the 
circular girders shown in elevation. The girders, again, are made up 
of diaphragm plates, connected to inner and outer angles, the former 
being riveted to the H beams, while the latter are similarly fixed to 
the tube plates. 

The work to be performed is somewhat asfoUows : — 

The first, and, for a time, the most difficult operation (owing to 
causes to be hereafter referred to) was the curving of the heavy 
plates. These, it may be mentioned, are 16 feet x 4 feet 4 inches, 
X 1^ and 1^ inch thick, and weigh from about 28 to 32 cwt each. 
The method now adopted is to bend them while hot in a large 
hydraulic press, from which they are removed, and allowed to cool 
slowly. When cold they are again placed in the press, and 
straightened finally. The edges and ends are then planed, and each 
plate is weighed, marked, and laid aside, ready to be placed on the 
tube when required. 

The longitudinal H beams are made up of a deep webbed tee and 
two angles, being partly drilled through these before erection. The 
circular girders are also partly drilled before being placed on the 
mandrel. These different parts form the main tube proper, leaving 
out the connections to skewbacks, the girder fixtures, tees, and 
other minor details, with which it is not at present intended to deal 

The tubes are built round about a mandrel, being supported 
therefrom by temporary connections, and drilled through the various 
parts, while in the exact form they are intended to be when finally 
erected. (See Fig. 2, Plate II.} 

This hasty sketch of the different steps of the work, required to 
be executed, will enable the details to be more clearly followed. 



On the Forth Bridge. 23 

The plates are heated in gas furnaces, of the style shown in Fig. 2, 
Plate III. The producer is close at hand, and from it the gas is 
led along the tube T to the box B, and thence distributed to the 
different furnaces by means of other tubes. 

The gas is admitted at the side^ as well as the back of each 
furnace. This, by the way, was an afterthought, to enable the 
plate to be more evenly heated, than when the gas was admitted at 
the back only, and it turned out a decided improvement. 

The escaping gases pass off through the flues G, which are highly 
heated thereby, and these in turn give a part of their heat to the 
incoming air, which is then passing along the flues A, on its way to 
the open furnace. 

The plates to be curved are heated to a dull red, after which 
they are withdrawn from the furnace by means of a hydraulic ram. 
To the end of the chain from the ram is attached a pair of tongs, 
made so that the greater the pull required, the grip is the firmer. 
The plate is withdrawn from the furnace on rollers, and run over a 
table into the hydraulic bending press, shown by Figs. 4 and 5, 
Plate III. A pressure of 800 tons is now applied while the plate 
is between a set of convex and concave blocks of the form necessary 
to bring it to the proper curvature. 

Almost immediately, on the blocks being separated, the plate is 
seen to be undergoing a change of form, and this so quickly, that it 
is quite perceptible to the eye. Sometimes the convexity becomes 
greater, while at other times it is the reverse. In all cases the plate 
warps longitudinally, this taking place principally at the ends. The 
distortions are most irregular and inexplicable, a plate seemingly 
under exactly the same conditions assuming a totally different form, 
nay perhaps the very reverse of that taken by the immediately 
preceding one. On being removed and allowed to cool, the plates 
gradually become in almost every case somewhat better, but scarcely 
ever sufficiently so as to be suitable for the purpose for which they 
are intended. 

Many methods were suggested, and tried, to overcome this warp. 
ing of the plates: thus, for instance, the edges were covered 



24 On the Forth Bridge. 

up, thereby allowing them to cool more from the centre ; another 
mode was to reheat and give them a second squeeze ; yet another 
was to allow them to cool partly, lying on a series of iron rollers, set 
to the true form the plate should take. These and others gave only 
very varying success. The plan finally adopted was to curve a 
quantity at a time, laying each plate, as it left the press, on the top 
of the immediately preceding one, with a layer of ashes between, 
and allow them to cool in piles of convenient size. When cold, 
each plate is again placed in the press, and straightened by means 
of repeated squeezes, strips of thin iron being placed above and 
under the points necessary to be brought to the true form. This 
answers the purpose admirably, and is the only method now in 
vogue. 

A somewhat striking incident happened during these preliminary 
trials. It arose out of an attempt to bend one of the 1^ inch thick 
plates while cold. During this process the plate cracked in several 
places, although the curve was only equal to that of a circle with a 
six feet radius. Samples of bending and tensile tests were cut off, 
and showed the plate to be of remarkably good material, and quite 
up to the specified quality. (See Fig. 3, Plate IV.) 

Mr Arrol attributed the failure to unequal cooling at the steel works, 
and this is borne out by the fact that different parts of the same 
plate are not uniformly easy or difficult to cut, but both these 
experiences are often found in a single plate. 

Mr Baker thought the failure of the plate to stand the bending was 
due to the fact that its edges and ends were not planed, but in the 
state they were in when they left the shears at the works. He had 
made a series of experiments with sheared and planed plates, and 
from the results obtained arrived at this conclusion 

Annealing removes satisfactorily both these objections, and in this 
lies the great benefit of bending the plates while hot, and allowing 
them to cool as described. 

The hydraulic press (see Figs. 4 and 5, Plate III.), for bending the 
plates, consists of a set of four 24in. cylinders G, resting on two cast- 
iron girders G, and supporting by means of two 7-inch wrought-iron 



On the Forth Bridge. 25 

columns, from each cylinder, a fixed table T overhead. On the top 
of the rams is placed another table T', which is raised and lowered 
in conjunction with the rams. Between these two tallies are placed 
the blocks B required to bend the plates to their particular form, 
equal in this case to a curve, the radius of which is six feet. The 
pressure brought to bear on the plates while being stamped, is about 
800 tons, provision being made for doubling this if necessary. The 
lower pressure has thus far been found sufficient for all purposes. 

After bending one of the first plates, it was kept between the 
upper and lower blocks for a few minutes, while it was yet hot. 
The consequence was that the side of the block next the plate heated 
much more rapidly than the other, or remote side. This induced a 
very heavy strain on the [metal, so much so that it broke the upper 
one completely through, at the same time giving a report somewhat 
resembling that of the discharge of a pistol. 

The plates after having been brought to their true form, as 
ahready described, are passed on to a large planing machine, as 
shown (see Fig. 1, Plate lY.), to be there planed on both sides. 

This is an ordinary planer, having*the table driven by a six-inch 
screw, but supplied with double cheeks, between which, on each 
side, is fixed the special tool boxes A A. The plate being operated 
upon, is placed on cast-iron curved blocks B, and held down to the 
table by means of bolts and draw washers, arranged so that they 
can be either quickly tightened up or loosened at will. Both tools 
cut simultaneously, and as the plate is being travelled backwards, 
as well as forwards. They are fed into their work, and reversed, 
by hand. 

When the sides have been planed, the plates are placed in an- 
other machine (see Fig. 2, Plate lY.), to be there planed on both 
ends. 

They are here supported from and held down to the table at one 
end in a manner similar to that adopted for the former machine, 
while at the other they are fixed by means of screws through the 
beam overhead. Wedges are also driven in lightly, at the sides, to 
prevent the plate being shifted sideways by the action of the tool 



26 OnAe Forth Bridge. 

while cutting. The tool box, and tool T are carried in a pendiilam 
P, receiving its motion from the travelling saddle S, by meaas of 
the connecting rod R Here also the tool is fed, and reversed, by 
hand. 

The pendulum P, and plates Q, have a series of holes H, each of 
which in its turn will be made a new swinging centre, to enable the 
tool to sweep the ends of the plates for the various sizes of tubes' 
After one end of a plate has been planed, it is reversed, and the 
finished end butted against a cast-iron face plate, set parallel to the 
plane of motion, of the cutting edge of the tool, thus making the 
two ends of each plate truly parallel, and thereby securing accuracy 
at the tube joints. 

Being now finished, each plate is weighed, marked, and placed on 
the pile with the nearest corresponding weight, ready to be removed, 
and built on the tubes, when required. 

In the shops the handling of these plates, as well as the rest of the 
heavier parts of the structure, is done almost wholly by hydraulic 
cranes of the style shown in Fig. 1, Plate III. In the ground 
there is placed a cast-iron box B, which carries the cylinder A. 
This again carries a mast consisting of two channels, having a hollow 
turned casting H at the bottom, and a solid one S at the top^ 
In the centre of the latter is fixed a pin, which allows the mast to 
turn, carrying with it the jib, as in an ordinary crane, but with 
this great difference, that it can make a complete circle. The jib 
is fixed to the piston rod P by means of cross-heads, which are 
at the same time made to carry the supporting wheels, running 
inside the channels of the mast, and bearing against the flanges, 
By this means the bending moment of the jib, and the weight 
thereon, are taken up, while the downward thrust is passed into the 
piston rod P. When loaded, the cranes are capable of handling 
fully two tons, with ease. 

The H beams, formerly mentioned, are built up of tee and angle 
bars. These have first of all to be straightened, which is accom- 
plished, in the case of the former, by means of a 15-inch hydraulic 
ram, and, in that of the latter, by an ordinary bending machine. 



On the Forth Bridge, 27 

All are then cut to the exact length of 32 feet, by a cold steel saw, 
moving with a velocity at the periphery of about 70 feet per minute. 

They are now ready to be built into cast-iron blocks on the drill- 
ing tables, and in building it is carefully attended to, that there is 
a distance of 16 inches between the different joints of the angles, 
while those of the tees are placed midway between those of the 
angles. 

To secure good butting, the end of each new beam about to be 
built is placed hard against the one already set up, and to which it 
will be joined when placed in the tube; that is, the end of the new 
one, is brought hard up against that of the old one, tee to tee, and 
angle to angle. 

Everything being now in order, drilling, and that through angles 
and tees at one and the same time, proceeds, by means of radials 
of the style shown (see Fig. 2, Plato Y.). When this part is 
finished, the beams are marked and laid aside till required to be 
placed in position, on the mandrels, where, as is evident, the joints 
will meet as fitted in the shop. Thus this section proceeds, beam 
following beam till the total length required is completed. 

It may be mentioned that, as regards the arrangement of the 
tables, they are placed on each side of the line of radials, which 
allows building up to go' on at the one side while drilling is being 
proceeded with at the other. 

To ensure accuracy in the form of the tubes, and also correctness 
in workmanship, the stiffening ci]:cular girders required (see Fig. 1, 
Plate II.) are built within a wrought-iron ring, the inside diameter 
of which is 12 feet, this being the mean size of the tubes at present 
under consideration. Within this ring, and at equal distances apart, 
are placed ten castings, each of which occupies the same relative 
position to the different parts of the girder as the longitudinal 
beams in the completed tube. These are also of a form suitable 
for carrying up the various parts of the girders while being 
drilled. When the girder has been built in this iron frame, all the 
boles are marked off to templet^ and afterwards drilled by a radial, 
the centre of the column of which coincides with that of the girder. 



28 On the Forth Bridge. 

Although some of the girders vary slightly ia diameter at some 
parts, according to whether they are off or on joint covers, this is 
easily overcome by fixing temporary packing strips against the 
ring to suit the new dimension to which they are of necessity built 
After drilling, the separate parts are all marked, removed, and now 
bolted together, awaiting erection on the mandrel. 

The angle iron rings for these girders are curved on a large cast- 
iron segmental block. A pin is fixed into the centre of this segment, 
round which a large wrought-iron arm carrying a curving wheel 
is moved. This wheel is of a form suitable to bear against the out- 
side or inside of the bar as may be required. When the angle is 
heated, one of the ends is grabbed behind the wheel to the segment, 
and the arm is now gradually moved round. The wheel bearing 
hard against the angle brings it close to the face of the segment, and 
it thus receives the proper curve. To assist the curving, a crow bar 
has to be used in front of the curving wheel to bend up the angle, 
while behind the wheel additional grabs keep it close to the 
segment. After the full bar has been curved in this manner, the 
grabs are removed and the wheel run backwards and forwards 
several times, and then it is ready to be removed, and with a little 
trimming up, fit to be used in any of the girders. 

Having now considered the principal parts which compose the 
tubes, the building and drilling of these will naturally follow. This 
work is done out in the open, on what is called the drill roads. 
(See rig. 4, Plate IV.) These are laid down to suit the drilling 
machines, and at such a distance and with such a length as to allow 
the bracing girders and connections thereto to be placed in position, 
as the work stands on the ground, prior to the final erection. 

The roads are so arranged as to be all equally suitable of 
access for the steam travelling cranes used in carrying the 
material to position, and in building the tubes. This is accom- 
plished by means of traversers, of which there are three, one 
in the centre and one at each end of the drill roads, those at 
the ends running on rails, at right angles, and close to the main 
roads, but fully twelve inches lower, while the centre one is run on 



an the Forth Bridge. 29 

cross rails, on the same level as the main roads. If it is necessary 
to change the position of a crane, it is run on to the traverser, and 
on it carried to the desired point, and there run off. In this way, 
the whole of the ground is commanded by the cranes. It has 
already been said that the material for the tubes is placed in position 
by means of these cranes, the work of building, as required in any 
of them, will now be described. 

Fig. 2, Plate II., shows the style of building. First of all there is 
the mandrel M, 45 feet long by 5 feet diameter, raised on iron 
trestles T, to a height, at the centre, of 10 feet from the ground. 
This corresponds with the centre of the outer rings of the drilling 
machines. 

The great length of mandrel required is to allow of its being 
carried up at the ends, when the H beams and plates are built in 
position. On this mandrel there are now secured, but in halves, 
temporary iron rings K, at the horizontal distance from each other 
of 8 feet. To these are fixed the radiating plates P, having holes 
punched in the outer end for bolting on the first part of the 
permanent work, viz., the inner angle A of the circular stiffening 
girders. The same bolts are also made to carry the web plates W, 
of those girders, on the outer edge of which is fixed the angle irons 
I, for making the final connection to the shell of the tube. The 
horizontal H beams H are now placed in position, being securely 
bolted through the inner angle of the circular girders. On these 
beams are now placed the shell or tube plates S, the ends forming 
butt joints, while longitudinally they lap one another, this taking 
place over the solid flange of the H beams. The end joint of the 
one plate breaks opposite the centre, or solid part of those on either 
side. The first plates to place in position are the inner, or those 
lying close against the flange of the beams, beginning generally at 
the bottom, and coming up on each side. Owing to the passing of 
the one plate beyond the other, one half of each remains free to put 
grabs and drawwashers on, without interfering with the placing of 
the outer ones in position. So soon as the outer ones have been put 
on, and fixed in a similar manner, there is passed round all a couple 



80 On the Forth Bridge. 

of angle iron rings, for binding and drawing them up to their 
proper position. The tightening up is done by means of iron 
wedges, between the plates and the rings. After the bottom plates 
have been fixed in position, the tube is borne up by wooden blocks, 
buUt between it, and the cradle underneath. 

The true position of the tubes, both as regards horizontal distance 
apart and height, is found by means of a theodolite, placed at one 
end of the roads, on a fixed platform, in a position such that when 
it is in line with a stationary point at the other end it always 
fixes the centres 120 feet apart throughout, and horizontally in the 
same plane. If the centre of the mandrel is not in this line, then 
it is made so by being raised, lowered, or shifted sideways to suit* 
When the mandrel is right, the tube must of necessity be so also, 
seeing the centres coincide. 

When the building of one ring of plates has been completed, the 
drilling machine is moved forward, the blocks in front being taken 
out of the way, and rebuilt behind, as it is travelled along. To 
enable the drilling to go on continuously, the building of the tube 
in front is being proceeded with, while the machine is still at work 
on the portion immediately behind. These tube drilling machines 
(of which there are four) are shown by Figs. 1, 2, and 3, Plate 
lY.). Each is self-contained, and on being run along the rails 
carries all with it The principal parts are, the wrought-iron under- 
frame or carriage A, on the one side of which is fixed the engine £ 
and boiler B, and two large cast-iron rings G, firmly bolted to the 
main cross girders. These rings have an internal diameter of 13 
feet, suflSicient to enable them to pass freely round the tube, when 
the machine is being moved along. Five cast-iron slides D are fixed 
thereon, and held in position by means of small elipper blocks F, 
fitting into a recess, in each of the rings C. On each of the slides, 
are the two heads H H. Each head is provided with a single drill, 
and is capable of being rapidly run from one point of the slide to 
another by rack and pinion gearing. The slides are kept in 
position, and also turned round the rings C, in either direction, by 
means of two worms W, carried in brackets F, one gearing in each 



On ihe Forth Bridge. 81 

ring in the circular racks E. These racks being bolted to the rings, 
serve also as guides, for steadying the whole upper portion of the 
machine. All the drills point to the centre of the tube, and having, 
as sho\in, both a circular and longitudinal motion, can with ease be 
made to reach every hole in any part of the structure, some of 
which are through a depth of as much as four inches of solid metal. 

It might be here mentioned, that some of the slides were 
specially designed to overcome the difficulty of drilling, say, a flat 
part in any of the tubes. The difficulty lies in the fact, that the 
drills on any of the fixed heads always point to the centre of the 
tube, whereas in the case just mentioned, the holes require to be 
drilled at right angles to the special or flat part. The mode 
adopted to overcome this was to make both ends of each slide 
circled, fitting them into separate heads, which in turn were bolted 
to the slipper blocks F, as in the others. On the head at one end is 
placed a worm, while on the same end of the slide there is keyed a 
wheel into which the worm is geared, by turning which the slide 
can be made to place and keep the drill pointing in any required 
direction. 

The whole of the drills are fed into their work by an automatic 
arrangement, the motion being imparted to the longitudinal shaft L, 
by a band driven of the main driving pulley. On this shaft slides, 
and by it also are diiven the worms W^, necessary for turning the 
worm wheel I, which at will can be made to drive the hand wheel 
E, thereby feeding the drill into its work. At one end of each of 
the main slides is overhung the driving pulley P, the power being 
transmitted from the engine to the whole of these by means of a 
cotton rope, guided where necessary by supplementary pulleys. 
The slack is taken up by a shifting quadrant Q, moving about the 
engine shaft as a centre, assisted by auxiliary pulleys on the wrought- 
iron frame close by the engine. 

When starting work on any tube, a drilling machine is moved 
forward to the point at which operations are to begin. Each of the 
five slides is now moved round the rings until the points of the 
drills face truly any series of holes in the longitudinal beams. The 



32 On the Forth Bridge. 

holes in this line, or series, are all drilled, two drills being at work 
on each line, then the slides are again placed so as to suit a new set, 
and so on until the whole of the tube commanded by the machine 
in its present position is finished. This is equal in length to 8 feet, 
and includes the full circumference of the tube. The number of 
holes in such is about 800, and the time required to drill all, when 
working continuously, is from 24 to 28 hours, varying thus much 
principally on account of the difference of thickness of the various 
parts of the tubes. The machine is in like manner made to drill 
the whole length of the tube. 

At several of the ends of the first four of these tubes are presently 
being erected the skewbacks, each a complicated connection of five 
different tubes, including one end of these just described, and also 
several heavy bracing girders. Into this, however, it is not pro- 
posed to enter at this time. At present other tubes are being 
treated in a manner similar to that already described, which shows 
if anything is yet required, that special work can only be grappled 
with to advantage by the free use of special plant. 

After the reading of the paper, 

Mr F. W. Dick said he had listened with very great pleasure to 
the paper read. As a steel maker he might be expected to refer to 
the cracked plate which had been so pointedly brought to notice, 
and the failure of which some people might wish to class with the 
mysteries with which it was the fashion at one time to surround 
steel. He thought it was due to the Steel Company of Scotland 
with which he was connectisd, to say that the plate referred to was 
not manufactured by them. He had no doubt that the cracking 
was due to internal strains which might have been occasioned by 
the plate being put out to cool in the wet in rainy weather. He 
had noticed in the Engineer of this week a letter to the Editor, in 
which the writer affirms that at the Forth Bridge Works the steel 
was treated in an extremely barbarous manner— he said, indeed, 
that it was most cruel treatment ; and also that if he had had the 
work to do, he would have left it to the steel makers. He (Mr 



On the Forth Bridge. 33 

Dick) did not know that steel manufacturers could curve plates 
better than they were being done hy Mr Arrol. He had no doubt 
that the writer of the letter had in his mind the rolling of the plate 
in long strips and to the proper curve, but he (Mr Dick) did not 
think that any steel maker would undertake such a job. The 
heating of the plates before bending was a beneficial measure. It 
prevented the danger of any failure of the plates from such causes as 
those to which the failure of this plate in question was due. It was 
really an annealing, and he thought the plates were treated in an 
admirable manner. The final setting of the plates after they had 
become cold was so slight that it would not set up much strain. 
A test piece from every one of these plates was brought to a cherry 
red-heat co6led in water, and then doubled up till the inner radius 
of the curve was 1^ times the thickness of the plate, so that the 
plate had to stand a bending test the same as was required by the 
fioard of Trade or by Lloyd's Registry. He thought they were very 
much indebted to Mr Biggart for his paper. 

The further discussion of the paper was adjourned till next 
meeting, when a vote of thanks was unanimously awarded the 
autlior for his paper, on the proposition of the President. 



On Energy and Entropy and their Applications to the Theories of Air 

and Steam. 

By Mr Henry Dyek, C.E., M.A. 



Received and Read 25lh Noumber, 1884' 



Introduction^ 

When I received an invitation from the Secretary to read a paper 
before this Institution, it occurred to me that I might give an account 
of some of the most recent applications of thermo-dynamics to 
problems connected with heat engines, and especially with the steam 
engine, as I found in looking over the Transactions that comparatively 
little had been done in that direction. It was, however, suggested 
to me that before entering into consideration of applications it might 
be well to give, especially for the benefit of the younger members, a 
resume of some of the more important formulae which occur in such 
investigations. In attempting this in the following paper I have 
avoided the detailed consideration of principles, and have simply 
shown how some of the expressions for air and steam may be 
obtained, with the object of affording a starting point from which 
investigations relating to their applications may be made. 

It is a well known fact that in the earlier days of the steam 
engine the most important improvements made in it were always 
the consequence of the discovery of some physical law, or property of 
steam, and that Sjneaton and Watt endeavoured to make their 
practice conform to what they knew of the principles involved, as 
nearly as possible as the circumstances under which they worked 
would permit. Notwithstanding the progress which has been made 
in recent years the same cannot be said of present mechanical 
engineering practice, for that is a long way behind the theoretical 



86 On Energy and Entropy, 

knowledge we possess, and the improvements which have been made 
seem to be due, not so much to keeping the principles of the action 
of steam clearly in view, as to the experience gained by a system of 
trial and error. This, of course, is to be accounted for partly from 
commercial considerations, but I am afraid it is chiefly due to the im- 
pression among engineers that the study of thermo-dynamics, however 
useful it may be as an intellectual exercise, and interesting as an 
accomplishment, is only of slight practical value. Hence we find 
that its laws have not hitherto guided practice to any great extent, 
but have rather been used to explain progress which had been 
accomplished after many experiments and trials. Such experiments 
and trials are of the utmost importance, and I have no wish to 
undervalue them in the smallest degree, but much time and money 
may be wasted if they are entered upon without a knowledge, at 
least, of the results of what has been done by others in the way of 
theoretical investigations, for science surely ought, if it be worth 
anything, to anticipate to a certain extent the lessons of experience. 
On the Continent, in recent years, much more has been done than 
in Britain to advance the knowledge of the practical applications of 
thermo dynamics to the theory of heat engines, and such works as 
those of Clausius, Zeuner, Him, Rontgen, Combes, Hallauer, Ledieu, 
and others are beginning to exercise a most important influence on the 
practice of mechanical engineering, an influence which will very soon 
reduce to zero the great advantage we have had in practical experi- 
ence, and in cheap coal and iron, unless we are prepared to go in for 
the more thorough study of the application of principles. For 
many years Professor Rankine's treatise remained the only one in 
the English language in which a theory of the steam engine founded 
on thermo-dynamics was given, but it is now known that from 15 
to 50 per cent, of the steam used in engines is not accounted for by 
his theory. D. K. Clark in England, and Isherwood in America, 
many years ago investigated the cause of this loss, but it is to Hirn 
that we are chiefly indebted for the advances which have been made 
on Rankine's work. 1 am afraid, however, that the results of his 
investigations are not well known to British engineers. Professor 



On Energy and Entropy, 37 

Cotterill, in his work on the Steam Engine, has given some account 
of them, as well as of some other experiments and investigations 
bearing on the subject, and thos has been able to show the progress 
made in the theory of the steam engine since Rankine left it, and 
this is almost all that has been done in Britain. The investigations 
of Hirn, Cotterill, and others, do not in any way lessen the value of 
Sankine's achievements, which must for ever be memorable in the 
history of science, but rather by making them more complete, place 
them more strongly in relief. 

Other fields of inquiry in connection with thermo-dynamics, in 
addition to what is included under the ordinary forms of heat 
engines, are gradually opening up. Machines worked with com- 
pressed air, and apparatus for cooling and freezing have made rapid 
progress in recent years, both in Britain and on the Continent, and 
these form almost the only exceptions to the statement that theory 
has not guided practice, for I think it will be admitted that without 
a knowledge of thermo-dynamics no such progress would have been 
possible. 

Investigations relating to thermo-dynamics are peculiarly appro- 
priate to an Institution which had Rankine for its first President, 
which has Sir William Thomson, Joule, ClausLus, and Helmholtz as 
honorary members, and which has now Professor James Thomson 
for its President, and as these men placed the laws of thermo- 
dynamics upon a firm basis, it is surely not too much to hope that 
the engineers of the Clyde will strengthen their position by taking 
gi'eater advantage of the assistance which a more thorough knowledge 
of these laws and their applications would afford them, and place 
before the Institution some of the results of their work. 

Section 1. — General Equations. 

The first law of thermo-dynamics, which expresses the fact that heat 

and mechanical energy are mutually convertible, is represented 

algebraically by the equation 

H = JQ (1) 

orQ = AH (la) 

6 



88 On Energy and EiUropy. 

where H represents the number of units of work required to produce 

Q units of heat. J is Joule's equivalent and A its reciprocal. 

If a number of operations be carried on at the same time this 

equation may be written 

H = J2Q (2) 

or since H may be either positive or negative 

H + J2Q = (2a) 

an equation which should be considered the generalised expression of 

the First Law. 

If the element of the external work done by an expanding body be 

represented by p dv, where p is the external pressure, and dv the 

increase of volume, then from this law it follows that if <fQ be the 

heat expended that 

JdQ = dH = dU+p(/i; (3) 

where dV is equal to the dynamical equivalent of the heat expended, 
minus the external work done. The quantity U is called by Sir 
William Thomson and Clausius the energy of the body, and is equal 
to what Zeuner and Cotterill call the inner or internal work 

Equation (3) is not generally integrable, but it may be made so by 
multiplying by a certain factor. It follows from the Second Law of 
Thermo dynamics that the reciprocal of the absolute temperature is 

such a factor, so that or — » a quantity which we will always 

designate by c^, is an exact differential. <^ is what is called the 
entropy by Clausius, the theimic weight by Zeuner, and the tliermo- 
dynamic function by Rankine. We will adopt the first of those names. 
If we have a source of heat at the absolute temperature r^, and a 
refrigerator at the temperature r^, and if JQi be the quantity of 
heat absorbed by any apparatus for converting heat into work, then 
the available energy, that is the energy which can be converted, is 
given by the expression 

J(Qx-Q.) = JQ.(^«) (,^ 

where Qg is the heat rejected by the apparatus. Equation (4) was 
first given in this shape by Sir William Thomson, but its principle 



On Energy and Entropy. 39 

was enunciated long before by Carnot, and hence is generally 
called Gamoffs Law of Efficiency, and for all practical purposes 
it may be considered the Second Law of Thermo-dynamies, In 
this form it shows the relation between the First and the Second 
Laws, a relation which is easily understood when we consider 
the case of the steam engine. By the First Law the dynamical 
equivalent of a given quantity of heat Q is JQ, while the 
Second shows us that only a fraction of this can be converted into 
work, a fraction which depends for its value on the relative tempera- 
tures of the boiler and condenser, and as the range between these 
two temperatures is necessarily limited, we cannot utilise all the 
energy which, according to the First Law, is resident in the fuel. 
The idea which naturally presents itself to those who know the 
First Law and are ignorant of the Second is, that heat being a form 
of energy, in a perfect engine the whole of it might be converted 
into work, that is to say that the actual work as measured by a 
brake on the crank shaft should be equal to the dynamical equivalent 
of the heat expended in the furnace. Such a view the Second Law 
shows to be entirely false. 

Equation (4) may be written in the form 

-Ti r^ (4a) 

from which we infer that the quantiiy of loork which can be perjoimed 
by a body is solely popoiiional to its absolute temperature. Him remarks 
that this is the most striking, clear, and simple statement of the 
Second Law of Thermo-dynamics. Clausius and Sir William 
Thomson extended this expression to the form 

^?-=« (4b) 

80 that if any body undergoes a complete cycle of operations of a 
perfectly reversible kind, as for instance in Camot's reversible engine, 
the algebraic sum of the quantities of heat it receives, divided 
respectively by their corresponding absolute temperatures, is equal to 
zero, or in other words the sum of the quotients is unaltered by 
the passage of the heat through the body. 



40 On Energy and EvUropy, 

If the temperature of the differeit parU of the working Babstanoe 
alter gradually during the process, then equation (4b) may be^written 

J T - ^ (4c) 

equation (4a) is simply the definite integral of this between the 
limits Tj and r,. 

If the cycle be non-reversible this equation is no longer true, for 
evidently then the left hand member is a positive quantity, if we 
consider heat taken in as positive, and suppose the engine to be one 
in which work is produced from heat, so that we may write 

J T=^ (4d) 

an equation which may be considered the genm'dlised expressicn of the 
Second Law of Themuhdynamics, 

The preceding explanations show us that the consideration of the 
quantities named in the title of the paper really embraces the whole 
field of thermodynamics, so that all that can be given in a single 
paper is a mere outline. It will be convenient to give, in the first 
place, a short resum^ of the usual analytical expressions for the two 
chief laws of thermo-dynamics, for details of which, however, special 
treatises or papers must be referred to, our chief object now being 
to show their applications to the properties of air and steam. 

An equation of the form / (;?,t;,T,) = 0, where p is the pressure, v the 
specific volume, and r the absolute temperature, may be called the 
characteristic equation^ and any two of these quantities may be taken 
as independent variables in the equations we form for showing the 
effects produced by heat. 

Consider first v and r as variables and p constant, so that when r 
becomes t + dr v becomes v + dv, dr and dv both being very small. 
Then the heat required to produce those changes will be 

dq = CvdT + k dv (5) 

where c» is the apparent specific heat at constant volume, and /« is what 
is usually called the latent heat of expansion. 

Taking^ and t as variables we have 

d(^ := CpdT + Ip dp ..(oa) 



On Energy and ErUfopy. 41 

whore Cp is the apparent ipecifie heat at constant pressure^ and Ip is a 
thermal capacity without special name. 

Lastly taking p and v as variables we have 

dq^Kdp + hp dv (5b) 

where hp and //« are thermal capacities without special names. 

The following relations exist between the quantities c^ c,, l^ h^ 
and h^ 

Cp'-C.^h (jj ^gj 

^'^^' (4) (6a) 

Cp^C,=—lp ^jj ^^^^ 

^ = '^ (I) (6c) 

and - _ /^t\ 

'^^ ^ \dv) (6d) 

By means of the last two expressions we may write equation (5b) 
in the form 

'^Q = '^(|) ^P + 'P (S)'^" (5c) 

The quantities Cp, c„ tic, are evidently partial differential co- 
efficients of U with respect to the different variables, and the follow- 
ing relations may be deduced. 
For V and t as variables, 

(57) - (3*7 = ^ (rfr) (7) 

Vorp and v as variables 

W) - \d^') = ^ (7a) 

or, since hp = e, (^), and K = c» (^). 

dp L*" \i)i ~ dv L"' U)J = ^ (7a) 

Lastly for p and r as variables 

(^) - (sv = ^ {£) .(7b) 



42 On Energy and Efdropy. 

We have in equations (7)^ (7a), and (7b complete analytical 
expressions of the First Law of Thermo-dynamics with diflferent 
independent variables. 

It follows from the Second Law (as already remarked) that the 
expressions for the qiiantities of heat given in equations (5), (5a)^ and 
(5b) are made exact differentials by multiplying them by the recip- 
rocal of the absolute temperature, and from this condition we obtain 
the following equations 

W~W"t (8) 

Comparing this with equation (7) we have 



or, 

T 



^7=A(t). 



{dy-^l^' (8b) 

''{£) = ^'(^d) (8c, 

similarly we obtain Ip- — At l^\ .^^. 

;(^"-(f)'.'.'r.'irr.'.'.<,.> 

(f ) - (^') = ^ = ^ b' (I) - *• (rf^)] (80 

Equations (8), (8a), &c., are complete analytical expressions of the 
Second Law with different independent variables. 

Substituting in equation (5) the value of k given in equation (8a) 
we have 

rfQ = c^rfT + At \Afdv ^j^j 

dH = JdQ==Jc.rfT + T(|)rf. ^^^) 

and similarly from equations (5a) and (8d) we have 

dK^Jdq^ Jcp dT - T (^j dp ^^^j 

By integrating equations (8c) and (8e) we obtain 

Jc,= & + T|(gf)d* (1^,^ 



On Energy and Entropy. 48 

^'"'^-^lilf^) * (lOa) 

The quantities k and k are called the reai dynamical specific heat at 
constant volume and constant pressure respectively, and they are the 
dynamical equivalents of the amount of heat required to raise unit 
mass through one degree absolute temperature, and are constant and 
do not depend on the state of aggregation of the body whether solid, 
liquid, or gaseous. The apparent specific heat, on the other hand, 
includes in addition to this the heat required to overcome molecular 
resistances and external pressures. 
From equation (6) we have seen that 

and from equation (8a) 

80 that 

Ar = (c,-c,)(|)(|) ^^^^^ 

and the pressure being constant, we have the equation, 

/dp\ 

/rfrX V^ 

^^' \dv) = -W\ 

w 

substituting in equation (10b) we have 

c, — Ce = — At \.\ . 

(^\ 

\dvj (10c) 

W (lOd) 

aud, /^\' 

. * w 

c„ s=. c- + At Vjf. 
(^\ 
\dvj (lOo) 



44 On Enerffy and Entropy. 

sabstituting in equation (Oa^ from equation (10) we have 

dU = WQ = [a + rj(g) dv] dr + r (|) d. ^,^^ 

and in equation (9b) from equation (10a) we have 

dR = J^Q = [k-rj(^:) dp] dr - r (^) dp (,j,j 

The first of these two expressions for the value of dR is the one 
which we will find most generally useful. Equating it with that 
given in equation (3) we have 

dR = dV +p.dv = [a + t|(^J) *] dr + T (I) d« ^j2) 

or. iU = fafr -H T 1(0) rf..* + [r g^ -^] rf. ^^^a) 

80 that U = const, -f J Wt + It l£) — p I dv .^^^ 

sa, however, in the applications of this equation we only require to 
know the variations of U, and not its absolute amount, we may 
neglect the constant and simply write 

U = |W. + J[.(|)_;,]* (120 

an expression which may be considered the general equation for the 
energy of unit mass of a substance^ v and r being the variables. 
From equation (11) we have 

^=£.*^%|(if)**^(D* „„ 

-'* + '^ (IS.) 

or, r.d<li ^dR = kdr + rM 

"*" *-»■»-* I' ''4(^* («b, 

for the same reason as in equation (12c) we may neglect the constant 
and write 



*-f't-J(^0* ,13. 

-""S-'-^KD* (.8d) 

- A log, T + F (ISe^ 



On Etiergy and Entropy. 45 

an expression which may be considered the general equation for the 
entropy of unit mass of a substance, v and r being the independent 
variables. Equation (18a) is sometimes called the General Equation 
of Thermo-dynamics, and from it we see that a given quantity of 
heat (in units of work) which a body receives, or gives out, during 
any infinitely small change of figure or dimensions, is expressed in 
every case by r,f14> where r is the absolute temperature, and d4> is the 
infinitely small variation of the entropy. The function F is what 
Bankine called the meiamorphic funcHon, r.dF being the quantity of 
heat transformed into mechanical work, whether external or internal, 
during an infinitely small change in the condition of the body, while 
the first part of the expression for the entropy, that is k log« r, we 
may consider the entropy of the sensible heat imported, and which 
causes change of temperature. 

We will now proceed to apply these general equations to determine 
some of the properties of air and steam. 

Section IL— On Air, Considered as a Perfect Gas. 
For a perfect gas since 

(g)-«,„d(^.« 

we see from equations (10) and (10a) that 

Jc.; = Kt,=sA; (U) 

and Jcp = Kp= k (14a) 

that is, the apparmU is equal to the real specific heat ; and since 

(g)=f."-(^)=M 

from equation (10b) we have 

Cf, — Cv = AIi (Ub) 

or, Kp — K^ = E (14c) 

^~ ^' "^ 77" (14d) 

the same results may of course be obtained by substituting 

(i)->^(t)-i 

in equation (10c). 

7 



46 On Energy and Entropy. 

If, in equation (12c)i we substitate 

A = K., andr(g) = p 

and integrate, we have for the difference of energy in the states 1 

and 2 

U,-U, = K,(t,_t.) (15) 

that iSy it is a simple function of the temperature. 

From equation (12) we have for the heat expended in raising the 
temperature of the gas from r^ to r, 

H = JQ = Jc« (Tg — Ti) -hj p.dv ^jgv 

Taking the indefinite integral of the general equation for the 
entropy (equation 13b) between the limits 2 and 1 we have 

*,-<A. = ^iog,;-;.j;(|)d., (,,^ 

and since in a perfect gas 

/dp\ R fdp\ Rt 



we have 



<^,-<^, = K„log,J + Rlog.J 



= K.[log.^; + (y-l)log.|] 



v^ (17a) 



_ (17b) 

Where 



7 
and since 

PlVi T, 



we have 



or, 



i<.g|-;+iog.^;=iog.;-; 
iog.^'=iog.;-;-iog.^; 



Vf 



substituting this value of loge - in equation (17a), we have 



»i 



^. - .^, = Kp log. J| - (K, - K.) log. ^' 



P (17c) 



On Energy and Entropy. 47 

.K,[.^j;-e--^).^a <„,, 

similarly substituting the values of log« -7 in the same equation, we 



have 



*,-<^, = K.[ylog.^| + log.^] (i^^j 

expressions which give us the di£ference of entropy for any two states 
of a gas. 

To apply these to special cases, suppose first, that the pressure at 
1 and 2 is the same, so that 

!!! „ L» 

Vi " T, 

and for 
Presgvre constant 

t^. (18) 



<A.-<^i = KplogeJ = Kplog,J 



T, 



when the 
Pottme is constant 

^.-^, = K,log.^; = K.log.g ^jgj 

when the 
Temperature is constant 

*.-♦. = (K,-K.Hog. I -^•' log. (^ (j„, 

= (K,-K.,l,g.a.^,<«.^} ,,^, 

hence, ^ — K, = ^ 

as already obtained in equation (14d) 

If we multiply equation (20) by r we have for the external work 
done during isothermal change of condition 

T («^, - <^,) - P.f, log. (J) = m log. (g) (^ob) 

from which we see that the amount of heat (in units of work) which 
is absorbed during expansion, or given out during compression, is 
equal to the difference of entropy into the absolute temperature. 



48 On Energy and Entropy. 

In adiabaUc expansion since no heat is given ont or absorbed we 
have 

so that _ „ _^ 

i_ 

v^ " \pj from eq. (17e) (21a) 



- = [^J from eq. (17b) (21) 



and V, ^ /My 



hence Ti __ /vA^ *__ ___ 

^."W ~W ' (21b) 

and the equation of the adiabatic curve is p,i; ^ = p^v,'^ = constant, 
and the external work done is 

y — 1 
substituting in terms of equations (21) and (21a) we have 

If we interchange the subscripts attached to the symbols in these 
formnlse they apply also to adiabatic compression of air. 

Sbotion III.— On Saturated Steam. 
If we apply the general equation 

.H.,^=Q^,J(^) .»]* + ,(!),. 

to the case of a body changing its state at constant temperature and 
pressure we obtain an expression for the amount of heat which 
becomes Latent. Under these circumstances the first term on the 

right hand side becomes zero, and the factor t l^\ of the last term 

is constant since the pressure and temperature do not vary, so that 
the heat expended, or the laUnt heat is (in unite of work), 

j<iH = L = T(g)K-.„) ^23) 

V and V being the volume of unit mass of the body in its first and 
second states respectively, t the absolute temperature at which the 



On Energy and Enh'opy, 49 

change takes place and I ^ j the reciprocal of the rate at which the 

temperature yaries with the external pressure. 

If the amoant of heat expended be estimated at the instant when 
the whole of a solid is liquified, we obtain the value of the latent 
heat of fusion or liquifaction. Professor James Thomson has made 
some interesting investigations relating to change of molecular con- 
dition. We cannot enter into details of those at present, but may 
remark that one of his conclusions follows directly from the last 
equation, although he arrived at it by quite another process of 
reasoning. That equation may be written in the form 

(dr\ _ T {y^ ~ rp) 

ydp)" L (23a) 

and it is evident in such substances in which the volume of a given 
mass in solid state exceeds that in the liquid state, that is when v^ 
is greater than i^j, as is the case for water and some other substances, 

then 17 I is negative, that is the temperature of fusion is lowered 

by increasing the pressure, a conclusion which was verified experi- 
mentally by Sir William Thomson. 

If the amount of heat expended be estimated at the instant when 
the whole of a liquid has been evaporated, we obtain the latent heat 
of evaporation, that is the heat expended in causing a body to 
change from the liquid to the gaseous state, and it is equal to 

L = Aii^j (v, — Vq) units of heat .^^^h) 

where v^ is the volume occupied by unit mass of the substance in the 
fluid state at the absolute temperature r^ and v^ the volume of the 
same mass when in the state of dry saturated steam. 

The value of i ^ j that is the rate of increase of the pressure with 

the temperature may be obtained from tables giving the results of 
Begnault's experiments, or computed from empirical formulas which 
have been formed to represent these. In practice, however, the 
value of the latent heat of evaporation is generally taken from tables 
or calculated from the empirical formula 



AO On Energy and Entropy, 

L » 1092 — 07 (T — 32°) 

= 966 — 0-7 (T° — 212°) (23c) 

the temperature T being in degrees Fahrenheit. From this expres- 
sion we see that L diminishes very nearly at the rate of seven-tenths 
of a onit of heat for each degree of rise of the boiling point. 

The corresponding expression for the total heat of evaporation, or 
the total heat of steam as it is usually called, being the quantity of 
heat required to raise unit mass of water from the temperature 
of melting ice to a given temperature, and to evaporate it at that 
temperature, is 

H=:1146 + -305 (T — 212°) (23d) 

a quantity which increases nearly at the rate of three-tenths of a 
unit of heat for each degree of elevation of the boiling point 

One of the earliest and most important applications of thermo- 
dynamics was the calculation by Kankine and Clausius of the 
volume, and hence the density of dry saturated steam, which can be 
obtained from equation (23b) since 

^Adr) (23e) 

Vi being the volume of unit mass of the steam, and Vq of the water, 

and the values of L, and l-£\ being known that of t'l can be com- 
puted. 

The results calculated from this formula agree very closely with 
Fairbairn's experiments, from which he formed the empirical formula 

389 

''""^^ ^i? + -35 (23f) 

V being the specific volume in cubic feet, and p the pressure in pounds 
on the square inch. This formula is nearly exact for pressures up 
to 100 pounds per square inch ; beyond that limit it gives too large 
a result. 

For purposes of calculation connected with steam engines the 
empirical formula 

pv^^ — const. 



On Energy and Eniropy. 61 

proposed by Bankine, is sufliciently exact. For pressures iu pouuds 
on the square inch, and volumes in cubic feet the value of the con- 
stant is about 475. 

The expression for the difference of entropy in any two states 
obtained from equation (13c) may be written in terms of the latent 
heat (units of work) thus 

^,-<^.=^Mog.:-;+^^*-^; ^^^^ 

an equation of great importance, but of which we will delay the 
application till we derive it in a more general form in which it can 
be applied to steam in any degree of saturation, for it must be 
observed that we have hitherto only considered dry scUwrated steam. 

In the case of supersaiurated steam, since it is not all in the same 
physical condition, the characteristic equation breaks up into two ; 
and we require an equation of the form 

/ (P.T) = 
and another for the specific volume in terms of either p or t, and the 
variable which expresses the proportion of pure steam, in unit mass 
of saturated steam. Let x denote this proportion, a quantity which 
becomes smaller the wetter the steam becomes. If f?^ be the volume 
in cubic feet of one pound of water, and v^ the specific volume of 
dry steam, then since each pound of wet steam contains x pound of 
dry steam and (1 — «) pound of water, the specific volume of wet 
steam must be 

V=zv^x + (l—z)vi (25) 

for ordinary temperatures, and when the steam is not very wet we 
may make 

V = ^a; (25a) 

an approximation which is often exact enough in calculations relat- 
ing to steam engines. 

The general equations which we have had for the effects of heat, 
although they hold for a liquid and its vapour, are not applicable for 
a mixture of the two substances such as wet steam, in which case we 
proceed as follows. If p be the common pressure of the liquid and 
the vapour, and L the ktent heat (in heat units) of the latter, then 



62 On Energy and Entropy. 

to change unit mass of the mixture from the condition denoted by 
the yariables x and r, to that denoted hyx-^dx and r + dr the heat 
required to be imparted is 

«jQ = L.dz + c" x.dT + c' (1 — x) dr (25b) 

where c' is the specific heat of the liquid c" that of the vapour. 
The specific heat used here is not that at constant volume, nor yet 
that at constant pressure, but is a compound quantity involving 
changes both of volume and pressure, and is the amount of heat 
required to raise the temperature of unit mass of either form of the 
substance one degree, under the condition that the two forms remain 
in equilibrium during the process. Thus c'' is that quantity of heat 
which saturated vapour requires to heat it through one degree, if the 
pressure is at the same time raised so that at the higher temperature 
the vapour remains in the same state of saturation, and in the case 
of vapour of water it is called the specific heat of saiuraUd stsam. 
The increase of pressure has very little influence on the specific heat 
c' of the liquid, since for such pressures as we consider the liquid is 
only slightly compressible. 
From equation (25b) we have 

^ = ^ = J [?f ^ +{c' + (c'-c') X} ^^] ^25c) 

bat tmcbft^ — is an exact differential, we have 

dT\r)- T (25d) 

80 that 

, _ dL L 
" -« -3? — f (26) 

and for the speafie heat of saturated steam we obtain the expression 

" ■•" rfr T (26a> 

which may be written in the form 

._dH L 

* ~dr T (26b) 

JTT 

where H is the total heat of evaporation, and j^ is the rate at which 



On Energy and KiUropy, 53 

H varies per degree of increase of temperature which in the case of 
dry steam we have seen is equal to -305, so that 

c" = -305 - ^ 

L ^ (26c) 

and as -for all practical temperatures must always be greater than 

•305, it follows that c" must be negative. From this wo infer that 
when dry saturated steam expands performing work, the temperature 
falls, and heat must be added to keep it in the dry saturated condi- 
tion, and conversely if dry saturated steam be compressed, heat must 
be abstracted in order to keep it from becoming superheated. For 
wet steam the value of H varies according to the degree of wetness. 
From equations (25c) and (25d) we have 

^ = "(7)-^«t <.;, 

integrating between the st:.tes 2 and 1 we have 



9» — 9i = ~:r~ — ~~' ■** ^ 



's 



T, 



Jr, -■ 



..(27a) 
the latent heat being in units of work in equation (27a), which is a 
general expression for the entropy which must be imparted to any 
mixture of a substance and its vapour, to change it from the state 
Tj a?i to the state tj x^. 

In the case of a mixture of steam and water c is sensibly equal to 
unity, so that we have 

^^ ^/ Tg ''"i '''1 (2'b) 

a result which might also have been easily obtained from the general 
equation for the entropy. If we suppose the steam to have been 
originally dry and to have remained dry, that is, that 0:3 = a^ = Jl, 
then we have equation (24). From equation (27b) we can easily 
obtain the amount of heat required to raise the temperature of steam 
in any state of saturation by a given amount. 

The applications of this formula are very numerous and important. 
We will only in the meantime consider one or two connected with 
the expansion of steam. As in this case the initial temperature is 
generally the highest, we may write 



54 On Enenjy and Knlvopy. 

♦.-♦.'^f-^:"'-^ J '<«•:-; ,«», 

If we suppose the steam to expand isothermally, so that 
Tiss Ti = T, and Li s L2 = U we have 

T (*, — >,) = L(x, —X,) (28) 

an expression which gives us the amount of heat which is required 
to be imparted to unit mass in order that the temperature may 
remain constant between the states 1 and 2. 

It is instructive to compare equation (28) with the corresponding 
equation for air (20b), as we then see why the quantity of heat 
required for a given change of state differs so much in the two cases. 

If the steam expand adiabalkally (/>i = <^,, and we have 

or, Ti L^iCa L^x^ 

Jlog -^- — — (,9^ 

as the equation of the adiabatic curve, for a unit mixture of steam 
and water of which r^xiis one point. 

The amount of water in the steam after expansion, when the 
temperature and pressure have fallen by a given amount^ is 

,.,j.[V.,„„^y ^^,^^ 

we may generally write (see equation 25a) 

V| = v^Xx, and Vjj - v^x^ 
so that V3 Dj 

where r is the ratio of expansion, Di the density of dry steam at the 
temperature r^, and D2 the density at r^,, therefore approximately. 

'^--.Wn.L^^+J^^S^J (29b) 

from which if we suppose xi = .la = 1, that is, that the steam is dry 
originally, and remains dry, we obtain the expressions given by 
llankino (Prime Movers p. 384) 

As, however, neither the one nor the other of these suppositions 
is usually true, the theory of the action of steam in the cylinders of 
engines, founded on them, leads to results which are far from correct. 



On Ene^rgy and Entropy^ 55 

The expansion curve for a mixture of steam and water may be 
expressed by an equation of the form 2^ = const., so that the 
external work 

--^['-Ci)"""] « 

Zeuner has shown that the value of n depends on the amount of 
water in the steam, so that if x represent the weight of water in 
100 parts of steam at the beginning of the adiabatic expansion, 
n = 1'135 — -001 X. 
For a: = n = 1-135 

a: a 10 » = 1-125 

ar - 20 /* = 1-115 

X = 30 n= 1-105 

from which we see that the curve approaches an equilateral hyperbola 
as the quantity of water contained in the steam increases. Rankine 

gave n = -^ for dry steam, but for that value the steam contains 24 

per cent, of water. He obtained this value from a large number of 
actual indicator diagrams, but he overlooked the initial condensation 
of the steam caused by the action of the sides of the cylinder. 
Grashof in his discussion of steam engines takes n = 1*125. 

Section IV.— On Superheated Steam. 

In considering the action of superheated steam, it is usual to 
assume that superheating has been carried to such an extent that it 
may be treated as perfectly gaseous, and therefore follows the same 
laws as those for perfect gases. 

Thus Kankine gave the equation 

»i; = 42140 - = 85-44 T ,«,, 

^ ^0 (31) 

where r is the absolute temperature of the steam, tq the absolute 

temperature of the water at the freezing point according to Fahren- 
heit's scale, p the pressure in pounds on the square foot, and v the 
volume in cubic feet. 

If ^ be given in pounds on the square inch then equation (31) 
may be written 



56 On Energy and Entropy, 

pP^-eiSr (31a) 

Rankine farther assumed that the total heai of the sUarn^ or as it is 
usually called in the case of superheated steam, tcM heai of gasefioi 
tion, is equal to the latent heat of evaporation at the freezing point, 
plus the heat required to raise the steam from that point to the 
temperature at which it exists calculated in the following manner. 
Taking equation (11a), viz.: — 

T# = dH = JiQ = [k - r |(j^') dp] dr - r (^i) dp (32) 

being the general equation ior the element of heat expended in 
terms of the temperature and pressure as independent variables, we 
have in the present case since the pressure is supposed to be constant 
and the steam to be in the perfectly gaseous state 

H, = K,(t. -T,) (32a) 

and when t^ = Tjj, 

Ho = Lo 
where Lq is the latent heat of evaporation in foot pounds, of one 
pound of the substance at the temperature t^^ so that for the integral 
of equation (32) we may write 

= Lo + 0-48 X 772 (T" — 32°) 
= 842872 + 371 (T* — 32) 

= 651)895 + 371 T foot pounds (32b) 

T being the temperature of the steam according to Fahrenheit scale, 
and T the corresponding absolute temperature. 

These formulsB possess the practical advantage of great simplicity, 
but it is evident from the assumptions which have been made that • 
they can only be considered as first approximations to the exact 
formulsB for superheated steam, and as the steam approaches the 
saturation point, the deviation from exactness is so great that they 
are no longer applicable. 

Difierent investigators have attempted to give expressions for 
steam, which will apply not^only to the superheated but also to the 
saturated condition when the necessary substitutions are made, but 
owing to the want of experimental data none of these can be con- 



On Energij and Enkopy, 57 

sidered perfectly satisfactory. We will consider shortly those of 
Zeuner,* which give results agreeing very closely with experiment 
and are not inconvenient for purposes of practical calculation. By 
taking advantage of some of our previous results we can somewhat 
simplify Zeuner's methods. 

The following fundamental equations which we have already 
obtained will serve as a basis for our investigation, 

"""*' -IKS)]-1W*)] 

^•00., A,= ,.-..)(D(^) ,, 

^•<'' JQ-a rfrt Ar(||)* (b)l III. 

^•« ■«} = », .r- A, (*)* 4 

and the condition eqmtion^ that is the equation which gives the 
relation of ^, Vy and t since the absolute temperature is a function of 
the pressure and volume is 

^' = (^) *-(*)* IV. 

We will assume that superheated steam is in a condition inter- 
mediate between that of a perfect gas and saturated steam, and that 
dry saturated steam is thus its limiting condition, that the specific 
heat at constant pressure Cp is constant, and that the relation given 
in equation (17d), viz. : — 

^-^.= K,[log,^;-5:^^log.J^] ^33j 

holds for superheated steam as well as for air, where y has, however, 
a difierent value from what it has in the case of air. As there are 
probably slight variations in the quantities Cp and y our resulting 
equations can only be considered approximate. 

From these equations and assumptions the following differential 
equation of condition is derived, 

* ZeitKchrift des Vereins (leutwher Tn^enieiire, Bd. XI. 



58 On Energy and Entropy. 

^#'(7— i)L ^ ^^ A y -p- ^...(34) 

of which the integral is 

pv^Br — Cpy (34a) 

where the constant 

Ay 
From Begnault's experiments we know that for snperheated steam 
Cp =8 0-4805 and y = 1'333, so that A being ^\^ we find B equal to 
51 nearly. The valne of C is found by assuming equation (34a) to 
hold in the limiting condition of the steam, that is when it is dry 
saturated, for which the values of the quantities v and r are known 
for a given pressure, say of one atmosphere, and thus we obtain 

j?» = 51 T — 192-5;?* (34b) 

p being expressed in kilograms per square metre, v in cubic metres, 
and r in absolute degrees Centigrade. This is Zeuner s formula. 
If, in equation (34a), we make, on the right hand side of the 

equation, 2? 7 = i;-«, we obtain 

pv = Bt — Ct;-« (34c) 

an expression of this form was given by Him* as representing the 
results of his experiments on superheated steam, but it can also be 
derived from theoretical considerations, as has been done in different 
ways by Hirnt himself, and by Schmidt,^ the constants, however, 
having different values from those in Zeuner's expression. Equation 
(34c) may be derived from Zeuner's if we consider as constant the 
specific heat at constant volume, in place of the specific heat at 
constant pressure. These expressions may be regarded as second 
approximations to the law of superheated steam, of which an expression 
of the form pv = Rt is the first approximation. 

Ritter§ has shown that the results of Hirn's experiments may be 

* Hirn — M6moire sur la Thermo-dynamique, 1867. 

+ Hirn — Theorie Mecanique de la Chaleiir, 1875. Tome second. 

X Zeitsclirift dea Vereins deutscher Ingenieure, 1867. 

§ Wiedemann'H Annalen, 1878. 



On Energy and Entropy, 



50 



-=-£ + 



represented by an equation of the form 

pc^ (34d) 

where B - ^i^^ and C = 28, when the pressure p is given in atmo- 
spheres, the volume v in cubic metres, and the absolute temperature 
r according to the Centigrade scale. This expression fulfils certain 
theoretical conditions of superheated steam more perfectly than the 
others, since the second term on the left hand side, which shows the 
variation from the first approximation, is a function both of p and r, 
while in that of Zeuner it is only a function of 2h <^d in that of 
Him and Schmidt it is only a function of r. As, however, Zeuner's 
expression is more convenient for purposes of practical calculation 
than the others, and is exact enough for such purposes, we will in 
the meantime confine our attention to it. 

If in Zeuner's expression p the pressure be given in atmospheres. 
V the specific volume in cubic metres, and r in absolute degrees Cent. 
pv = -0049287 T — •187815;?* (34e) 

The results calculated from this equation agree very closely with 
the results of Hirn's experiments on superheated steam, as is shown 
by the following short table : — 



Pressore 
in 


Temp. 
Cent. 


Specific volumes in cnbic metres. 


Atmo- 
spheres. 


Hirn. j Equation (34c). 


i- 

^ 4 
4 
4 
5 
5 


118-5 
141 

200 

165 

200 

246 

162-5 

205 


1-74 

1-85 

697 

0-4822 

0-522 

0-5752 

0-3758 

0-414 


1-7417 
1-8526 
0-6947 
0-4733 
05164 
0-5731 
0-3731 
0-4160 



If p be in pounds on the square indi, v in cubic feet, and r in 
absolute degrees Fahr. then 



no 



On Knerfiy and Entropy. 



pv = -645 T — 23'Spi (34f) 

By comparing this with equation (31a) we see clearly the difference 
in the results of Rankine and Zeuner's suppositions. Multiplying 
by 144 we obtain the product 2>^' in foot pounds. 

If in equation (34f ) we substitute for t in terms of p from the 
results of Regnault's experiments and apply it to find the specific 
volume of dry saturated steam at constant pressure, we obtain results 
which agree with those got by the ordinary formulae, as is shown in 
the following short table :— 



Absolute 


Specific volumes in cabic feet. 

■ 


Pressure in 
lbs. per 










square iach. 


Ordinary formula 


Equation (840- 

1 


14-7 


26-37 


1 
26-40 i 


30 


1348 


13-43 1 


60 


7-02 


700 


100 


4-34 


4-83 


150 


2-96 


2-91 


200 


2-26 


224 



(a) 

(b) 
(c) 



}...{So) 



From the fundamental equations III. the following expressions 
may be deduced, 

"^^^ = :5^izri y ^^P + yp ^^A 

JrfQ = Jc, (rfr ^IZllUp) 
JrfQ = JCp Ur + (y _ 1) I. d^ 

These are the well-known equations of Clausius and Zeuner for perfect 
gases, but when applied to superheated steam the values of c,, c„ and 
y are (as already remarked) different from those for such gases. 
Taking the general equation 

rfQ = ArfU + A^ dv 
arid substituting from equation (35a) we have 
A 



On Energy and Entropy. 61 

integrating this from a given initial condition we have 

A(U-U0 = :5^:^l(i^^•-i>xt'l) (3e^) 

if we assume the initial condition to be that of water at 0°G. then 
A (U — U,) gives the increase of what is usually called the steam hea^ 
by Continental writers, and denoted by S, and we have 

s = So + ^^:3Yi?» (3gb) 

So being a constant to be determined by applying the equation to 
the case of dry saturated steam, and is found to be equal to 858. 
If we add to this the heat equivalent of the external work Apv we 
have for the total heat of unit mass of the steam 

= So+c,(T-g^') (S6c) 

858 + -4805 T — 17-7jp* units of heat (36d) 

= 662376 + 371 T— 13664 |>i units of work (36e) 

the temperature being absolute according to the Fahr. scale, and^ 
the pressure being in pounds on the square inch. This expression 
shows that for such pressures and temperatures as are used at present, 
Sankine's formula does not differ much in its results from those 
given by Zeuner's. For higher pressures and temperatures, however, 
the latter is the more exact, and, moreover, it has the advantage of 
being applicable to temperatures down to that of the saturation 
point. 

When equation (36c) is applied to dry saturated steam (substitut- 
ing for r in terms of ^) it gives us the total heat, and the results thus 
obtained agree very closely with Begnault's experiments, as is shown 

in the following short table : — 

9 



62 



On Energy und Entropy. 



Abtfolate 
Pressme in 

Iba. per 
square inch. 



14-7 

30 

60 
100 
150 
200 



ToUl Heat. 


Iiegnaalt*8 
EzperimenU. 


Equation (36d). 


1146-60 
1158-28 
1171-17 
1181-86 
1191-20 
1198 34 


1146-08 
115822 
1170-85 
1180-96 
119115 
1196-32 



These results do not pretend to exactitude beyond the first 
decimal figure. 

The general formulse we have had may be applied to the different 
problems connected M'ith the expansion and heating of superheated 
steam under different conditions. We have only space to notice 
one—that of adiabatic expansion. In this case we place JdQ = in 
equation (35a), and then 

V dp + yp dv = 



or. 



dp dv 

-^ + y - : 
j) ' " 







integrating between the limits (piV^) and (p^r,) we have 

Pi ^ V 



or, 



P2 VI 

Pf \V (37) 

hence PiV\y = poV^y = &c., as in the case of air, only for superheated 
steam y = 1-333. 

If we compare this equation with the corresponding one for 
saturated steam, we see that in superheated steam the adiabatic 
curve approaches the axis of abscissae somewhat more rapidly than 
that for saturated steam. 

The external work done by unit mass of the steam is 

'^'^.t-fen „ 



On Energy and Entropy. 63 

We have now considered as far as is possible, within the limits of 
a single paper, how the chief formulae used in thermo-dynamical 
investigations are obtained. A systematic treatise would, however, 
be necessary to do the subject justice. Although some of the 
methods adopted have, from want of space, suffered from undue 
compression, I hope the results given will serve as a basis for the 
future discussion of the applications of thermo dynamics to problems 
connected with heat engines. 

On the motion of the Presfdent, a vote of thanks was cordially 
awarded Mr Dyer for his paper. 



On Mr ManstVs and the hU Mr Fronde's Methods cf Analysing the 
BesaUs of Progressive Speed Trials. 

By Mr William Denny. 



(see plates VI., VIL, VIIL, IX., X., XL, XIL, XIIL, XIV., XV., XVL, 

AND xvn.) 



Received and Read 23rd December , 188^. 



In the spring of the present year, Mr Bobt. Mansel issued a pamphlet 
(see p. 102) in which he criticised with considerable severity some 
remarks I made in the discussion of a paper read by the late Mr 
William Proude before the Institution of Naval Architects, on the 
7th of April, 1876. As Mr Mansel addressed this pamphlet to the 
President and Council of this Institution, it seems a right and 
proper thing that any reply should be made before the members, 
which will give as much publicity to the reply as Mr Mansel, by a 
wide circulation, gave to the pamphlet. On the 14th of May I 
addressed a letter to Mr Mansel, acknowledging receipt of his 
pamphlet, and on the 9 th of the following month I wrote to him 
again, intimating the manner in which I proposed to deal with it. 
From the first of these two letters I make the following quotation, 
as it deals with a point in Mr Mansel's criticism against which I 
thought it was necessary to protest promptly. I said:— "Even, 
however, from the short perusal of your letter, I gather that you 
consider my remarks to have been made in some underhand way, 
and, as it were, behind your back. To this I feel compelled at once 
to demur. What I said was said publicly, and before a public 
Institution. Indeed, as the Institution of Naval Architects is 
exclusively devoted to Naval Architecture and Marine Engineering, 

10 



66 On Progressive Spud Trials. 

and, I believe, the only Inatitatiou in this country exclusively 
devoted to these subjects, it never occurred to me that its proceed- 
ings would be unknown to a professional man of your high standing. 
Whatever points there may be for discussion between us, I hope you 
will understand that your failure to learn of my remarks made in 
1876, is not a matter for which I am prepared to accept any blame." 
These sentences sum up my reply to this portion of Mr Hansel's 
criticism, and I shall add nothing further to them now. 

Mr Mansel condenses the statements which I made in the discus- 
sion by saying, that they amount to : — '' E. Mansel, taking advantage 
of a private communication to him of a discovery of Dr Froude, had 
devised another means of representing the same idea, and proffered 
it to Mr William Denny as his own discovery." I do not think any 
one who reads my remarks as they are quoted in Mr ManseFs Letter 
of Reclamation will take such a meaning out of them. What I said 
amounted to this — that, in a conversation with Mr Mansel, I had 
conveyed to him Mr Froude's idea of determining the initial friction 
by reducing the indicated horse-power curve to a curve of indicated 
thrust, and prolonging this curve to the vertical axis raised from the 
speed zero. In reply to Mr Froude, I said : — " I do not think Mr 
Mansel originally did more than proceed on the notion I had given 
him of what you had done, and I believe he forgot all about where 
the notion came from, which is common enough for all of us to do. 
I have, myself, occasionally borrowed from my friends, but when I 
have been reminded of it I have acknowledged it, although I could 
not say at the time where the idea came from." This is a very 
different statement from accusing Mr Mansel of taking advantage of 
a private communication. When any great subject is under discus- 
sion, and wlien ideas about it are prevalent, it is often very difficult 
to determine to whom the credit of their origination should be given,, 
and it is often as difficult to determine whether they originated 
spontaneously in several minds at once, or were conveyed from one 
mind to another by suggestion. At the time I made the statements 
which Mr Mansel has quoted I was under the impression that the 
idea which I conveyed to him had lain in his mind, and was the 



. On Progressiv'y Speed IVials. 67 

seed from which germinatied his method of dealing with the initial 
friction. I have had a most careful search made into every scrap of 
evidence which might indicate that Mr Mansel originated his method 
of dealing with the initial friction previous to my conversation with 
him in the autumn of 1875, but I cannot find any such indication. I 
have found one letter from Mr Mansel on the subject of the trials of 
the " Hawea '* and *' Taupo," which he addressed to me on the 17th 
of May, 1875, and in which he speaks of the initial friction, or 
rather the pressure necessary to work the engines unloaded, as being 
probably the cause of the differences between the trial results of 
these two steamers. Any one who will carefully read this letter — 
printed in the appendix — will observe that Mr Mansel did not show 
any way of determining the amount of the initial friction, but made 
two arbitrary corrections, and that at the two extremes of speed, 
upon the five pounds which he had allowed for it. He thus made 
the results of his analysis square with the trial results. If Mr 
Mansel can bring me any proof that he had worked out the idea 
expressed in his paper, read before this Institution in March, 1876. 
previous to the conversation which we had in the autumn of the 
year before, then I shall admit that I was mistaken in my impression 
about the matter. If the idea of defining the amount of initial 
friction from a line passing through force ordinates as distinguished 
from power ordinates, which underlies the continuation of the indi- 
cated thrust curve and the continuation of the straight line passing 
through the logarithms of the corresponding pressures in the cylinder, 
occurred to Mr Froude and Mr Mansel independently, then I shall 
have pleasure in acknowledging that I was mistaken. At the time 
of the discussion I was under the impression that Mr Mansel had 
taken the idea of working with piston pressures from my conversa- 
tion with him Wherever I spoke under this impression I admit 
myself in error. Mr Mansel had the idea of using piston pressures 
from the first, and he also knew that initial friction must be an 
element in the power developed. What Mr Froude showed me 
when I met him at the meeting of the British Association at Bristol 
in the autumn of 1875, was that by means of the indicated thrust 



68 On Progi'esrive Speed Trials. 

carve it was possible to determine the amount of this initial friction. 
It was this idea which I discussed with Mr Mansel in the conversa- 
tion to which he refers, and it was the possibility of so determining 
the initial friction from the indicated thrust curve which he 
rejected. On the occasion of our meeting, Mr Mansel denied the 
possibility of so obtaining the initial friction. His statement — 
** There is more than friction, I can prove it/' I do not remember to 
have heard. I do not wish to be too severe in commenting upon 
any of the expressions used by Mr Mansel in his Letter of Beclama. 
tion, but there is one to which I must draw the attention of this 
Institution. On page 4 of his pamphlet, at the end of the first 
paragraph, Mr Mansel says, referring to myself — " I never, however, 
imagined his misunderstanding would have carried him so far as to 
necessitate a public proof of his having made himself ridiculous 
about a fallacy !" I do not think this fit language to use in contro- 
versy, and it is my purpose throughout this paper, and any discus- 
sion which may follow upon it, to use this sentence as an indication 
of what should be avoided and not as an example to be followed by 
myself, or, I hope, by others. 

When Mr Mansel began to analyse the progressive trial results, 
which he found in my paper of March, 1875, he did so in ways 
which in many points differed from his later analysis. He began 
with the attempt to correct the Admiralty formula connecting area 
of midship section, indicated horse-power, and speed, by substituting 
a better measure of resistance for the midship area, and by differ- 
entiating in the power an assumed value for the amount of the initial 
friction. After the discussion closed he added a memorandum to it, 
splitting up the indicated horse-power into six different items. 
Three of these were factors. 1st — the factor involving initial friction, 
or the pressure necessary to work the engine unloaded ; 2nd — the 
factor for slip; and 3rd — the factor for friction due to the working 
load. Dividing the gross indicated horse-power by these three 
factors, he obtained E^, or the effective power. This he split into 
three terms — E,, the power due to the skin friction of the wetted 
surface of the steamer; E„., the power due to the movements com- 



On Progressive Speed Trials. 69 

mnnicated to the fluid in the vicinity of the steamer ; and E„ the 
power recovered from the wake hy the propeller — a quantity which 
was deducted from the sum of £f and E„. Mr Mansel calculated 
the amount of each of these elements by allowing for the constant 
decrement of the pressure five pounds per square inch on the high- 
pressure cylinder, for the friction due to the load yV^^ of the residual 
power, and for the slip a percentage of the residual power correspond- 
ing to the slip percentage. £, he calculated by an approximate 
estimate of the wetted surface, and a formula of Beaufoy's ; E„ he 
calculated by a formula founded on Poncelet's principle of investi- 
gation. Er at first he allowed as equivalent to ^ Ef, but this giving 
rise to some discrepancies in the results, he calculated — only by a 
more complicated formula — the value of E, as well as the values of 
E„ and Ef . The result of these various calculations was the produc- 
tion of figures which very closely agreed with the experimental trial 
results of the " Goa" and "Africa." These are the methods with 
which Mr Mansel began in 1876. In 1876 he changed to a very 
different method, under the impression that he had discovered 
constant laws for the revolutions, pressures, and gross developments 
of power, true for each steamer, although differing between steamer 
and steamer in the values of certain quantities, which are constant 
for each steamer. He still mentions at the end of his paper his 
original analysis of power, but thereafter this portion of his investi- 
gation shrinks iu amount and diminishes in value, absorbed by the 
theories of the straight lines. The leading elements of his 1876 
paper are the revolutions and the piston pressures, and their com- 
bination in the gross power, On the underside of a speed axis he 
sets down as ordinates the logarithms of the speeds and so constructs 
a curve. Setting up from this curve at each of the speeds the 
logarithm of the corresponding revolutions he obtains a straight 
line. On the logarithms of the revolutions he sets the logarithms 
of the piston pressures at the various speeds, and he obtains another 
straight line inclined to the base line of revolutions from which it 
has been plotted. The pressure corresponding to the logarithm at 
the zero of these two lines he calls the constant decrement. For the 



70 On Progresrivi Speed Trials. 

purpose of this paper, aa the points in discussion with reference to 
Mr Fronde's work relate to pressures, it is unnecessary to take in the 
question of the revolutions, and the gross power, or even the residual 
pressures subsequently introduced. In bringing Mr Mansel's theory 
to the test of a larger experience than it has yet touched, I shall 
therefor^ start from the basis of proposition No. 1 in his paper read 
before this Institution in March, 1876. This proposition is as 
follows : — *^ Experimental law of the pressures. — If a steam vessel be 
tried at various speeds, and if along an axis, at points representing 
the speeds, parallel lines be laid off, upwards, representing the 
logarithmic values of the corresponding piston pressures, the ends of 
these lines will range in a straight line slightly inclined to the axis, 
and having its ordinate at the origin, equal* to the logarithm of the 
statical friction of the machinery.'' In this proposition Mr Mansel 
caUs the ^'constant decrement" the ^'statical friction of the 
machinery." I hope he will permit me to use the words of Mr 
Froude, and to call this quantity for convenience during the 
remainder of this paper ** initial friction." 

On page 5 of the Letter of Reclamation Mr Mansel says: — "I do 
not doubt that Mr Denny honestly believed that Dr Froude's method 
and mine were alike at bottom, and gave the same result, and in 
this belief he repelled any explanation" I am surprised at Mr 
Mansel making this statement, when what I really said as quoted by 
him on page 2 of his Letter of Reclamation was : — '' You will see 
that a different method of analysis has provided us with, although 
not an exact confirmation, yet a very close confirmation of what Mr 
Froude has said." Any one who reads my remaiks will see what I 
meant was this — ^that while the general idea in Mr Mansel's method 
of finding the initial friction corresponded with the general idea 
upon which Mr Froude had worked, the methods were different, and 
the results were also to some extent different. I have compared 
their results by the values found for them in a selected list of pro- 
gressive measured mile trials which was compiled for the following 
purpose. My firm constructed about two years ago an experimental 
model tank very similar to that erected for the Admiralty by the 



On Progressive Speed Trials, 71 

late Mr Froude at Torquay. As soon as we got it into working 
order, and had organised its experimental staff, we determined to 
go back upon our data of progressive trials, and to analyse them by 
its means. For this purpose early in last year a list was selected of 
those which were most faultless in the matter of propeller immersion 
and weather. No trial was put upon this list in which the weather 
was not of such a nature as to permit reliable results to be obtained, 
or in which the propeller was not fully immersed. From this list I 
have further omitted, for the present purpose, all ships for which the 
number of double runs on the measured mile was less than four. So 
far as the accuracy of observation is concerned, all our trials are of 
equal value, as they are all conducted by a numerous and well trained 
staff. It is fairer to test Mr ManseFs later formula by such a 
selected body of results, than by the total number of our progressive 
trials, in which there are many of doubtful or secondary value 9 
owing to the nature of the weather or the immersion of the propeller. 
On Table I. in the appendix will be seen the extreme differences in 
the percentage ratios of the initial friction expressed in indicated 
thrust to the maximum indicated thrust exerted during the trial. 
By Mr Froude's method the highest ratio is 18*5 per cent., and by 
Mr Mansel's method the ratio for the same ship is 8*8 per cent., 
while the highest ratio is 10*6 per cent., the lowest ratio is by Mr 
Fronde's method 2*8 per cent., and by Mr Mansers 17 per cent. 
It will be observed that in constructing this table use is made of 
piston pressure as well as of indicated thrust. In the diagrams of 
curves indicated thrust alone is used. The 30 trials used in the 
table are arranged in three divisions. The first of these contains 
those vessels of which the lines of indicated thrust, set off in logar- 
ithms, come most nearly to Mr Mansel's straight lines. They corre- 
spond to the illustrations given in Fig. 4, Plate YIL The second 
division corresponds to the illustrations given in Fig. 5, Plate 
VII., and includes those steamers of which the lines of indicated 
thrust, set off logarithmically, diverge further from straight lines 
although still capable of being fairly continued to the speed 
zero so as to give some measure of the initial friction. The 



<f2 On Progressive Speed Trials, 

third division, corresponding to Fig. 6, Plate VII., contains those 
steamers of which the indicated thrust lines set off logarithmically are 
so irregular in curvature that they can not fairly be continued to the 
speed zero. Twelve steamers are included in each of the first and 
second divisions, and six in the third division. Although there is a 
very real similarity between the methods of Mr Mansel and Mr 
Froude there is a considerable difference in the reasons which each of 
these gentlemen has given for his method. From Mr Mansel's Letter 
of Reclamation it is evident he misunderstands Mr Froude's method 
and in so strange a manner as to leave the impression that he never 
took the trouble to make himself acquainted with Mr Fronde's ideas 
upon the subject Mr Froude started with the knowledge, which he 
had obtained from his experiments, that skin friction varied pretty 
nearly as the square of the speed, or more exactly as the power 1*87. 
He inferred that the lower portion of the indicated thrust curve might 
be safely continued according to this power of the speed, because in 
all steamers at the lower speeds the surface friction constitutes very 
nearly the entire resistance. As the curve rises above these low 
speeds the other elements of the resistance involved in the formation 
of waves and eddies begin to make themselves felt, and increase the 
resistance in a very much greater ratio than the square of the speed. 
In the letter which Mr Mansel received from Mr Froude, and which 
he so frequently quotes, this is made abundantly clear, as is shown, 
by the quotation on page 12 of the Letter of Reclamation, where 
the following remarks occur : — ^' The meaning of all this is that, as 
a matter of fact, the resistance of the ' Merkara ' is practically as tho, 
square of the speed, up to quite 9 knots, above this speed, the 
resistance increases in a higher ratio, and then of course for higher 
speeds deviates from the parabola, which correctly expresses it so 
far.'' Mr Mansel must have had this sentence before his eyes in the 
composition of his Letter of Reclamation, and yet on page 7 he 
writes as if Mr Froude would use the square of the speed throughout 
the whole range of the speeds. This imputes to Mr Froude an idea 
which had no place in his mind. Mr Froude knew very well from 
his model experiments that resistance curves in no case followed the 



On Progressive Speed Trials. 73 

supposed law of the square of the speed, excepting in sach portions 

of ihem as came within the dominating influence of skin friction. 

Besides^ confirmatory proof, from progressive trials, of the fallacy of 

this square of the speed theory had been furnished by myself in the 

paper which I read at Bristol before the British Ajssociation in 1875. 

In this paper I showed that the corresponding theory of the power 

required to overcome a vessel's resistance varying as the cube of the 

speed was quite untenable. Having on page 7 of his Letter of 

Beclamation assumed for Mr Fronde the notion of the resistance 

varying continuously as the square of the speed, it was very easy 

for Mr Mansel to bring this notion to a reductio ad ahsurdum, and to 

write the following sentence on page 8 : — "But in this Dr Froude 

simply begs the qwsUon for he had no more right to assume this value 

than the 4*06 of the pair above, and the obviously absurd — 2*09 of 

the upper pair.'' In the same vein Mr Mansel continues — " It is 

true, a limitation is laid down that ' the resistance is not to outrun 

the square of the speed,' which amounts to sayiug that the method is 

not applicable to a steam vessel at all ; for I not only deny, but can 

offer most satisfactory proofs that in no instance does this assumed 

law, of resistance varying as the square of the speed, hold good." 

It is very easy to defeat an opponent, however great that opponent 

may be, if you are at liberty to make his opinions for him. Mr 

Froude based his continuation of the resistance curve upon his 

knowledge from a very large number of experiments, most accurately 

performed and observed, that at low speeds the resistance of any 

steamer was composed almost entirely of skin friction, the law of 

which he had also discovered by experiments to be a variation 

according to a power of the speed ranging from 1-83 to rather over 

2. Mr Froude, in this same letter to Mr Mansel, gives a tabulated 

comparison with a group of pressures deduced from his own method 

and also from that of Mr Mansel. He carries this comparison the 

length of 10 knots, and I assume he carried the comparison to this 

point because it was the next whole figure above 9*2, one of the two 

lowest determined speeds. But he did it also for the purpose of 

showing that the error in the assumption of the square of the speed 

11 



74 On Progressive Speed Triak, 

began to tell above 9 knots, as will be found in a quotation made 
from his letter on page 12, which is as follows : — " The curve calcu- 
lated by the equation P = a + b V*, cuts exactly the two points of 
pressure given by the 'Merkara' experiments, for the 6-2 knots and 
the 9*2 knots. This, of course, it was bound to do, because it was 
calculated from them; it, however, cuts below the point which 
belongs to the 11-09 speed, and still more below that which belongs 
to the 12'91 speed." It is quite evident from this that Mr Froude 
did not intend his comparison to be carried at the outside beyond 
10 knots, nor do I believe he intended it even to be carried so far, 
excepting for the purpose of demonstrating the variation which 
began to take place between it and the curve deduced from the 
experiments. Yet, in the face of all this, Mr Mansel carries on the 
square of the speed up to nearly 13 knots, and in doing so furnishes 
himself with what he fancies is a crushing argument against the 
method of Mr Froude. On page 11 Mr Mansel writes as follows: — 
''It is obvious, from 13 knots to 3, according to Dr Froude's figures 
for this last speed, there is as perfect agreement as could be expected 
between the formula values and the experimental. Now, from its 
nature, this curve of mine must develope into a straight line when 
the logarithmic ordinates are set up to the speed abscissas, and upon 
no reasonable principle can it be contended that the law giving a 
straight line from 13 to 3 knots should not continue true for the 
remaining three knots ; and thus by going to the origin we get the 
value of m belonging to the limits of experience. It is, however, 
a matter of certainty that experiments made between the 6-2 
knot speed and zero, would have shown a change of value of m due 
to changed circumstances explained &s the lower conjugaJU solution. 
The value of 10*04, however, being derived from the 9*2 and 6*2 
knot speeds, is not in any way connected with the unknown region 
under the 6*2 speed, and consequently, is neither true for the 
experimental nor the unknown lower speeds with the steam vessel 
Dr Froude's curve is hopelessly erroneous at the higher speeds, and 
is only true for the 9-2 and 6*2 speeds, because he compelled it to 
take the true values at these points." Of course, Mr Froude's curve 



On Progressm Speed Trials. 75 

ifl hopelessly erroneous for the higher speeds if it is made out in 
direct contradiction to Mr Froude's ideas, and the explanation given 
by him in his letter to Mr Mansel. Mr ManseFs assumption " that 
upon no reasonable principle can it be contended that the law giving 
a straight line from 13 to 8 knots should not continue true for the 
remaining three knots " is an assumption and nothing more, based 
upon his happening in the case of the '' Merkara" to have hit upon 
a straight line. It must, also, be remarked that the experiments 
justifying Mr Mansel's straight line range only from 13 to 6 knots. 
They do not extend to three knots. Is it possible that Mr Mansel, 
after condemning Mr Fronde's method, went to three knots on the 
ground of their agreement down to this point 1 Mr Mansel considers 
the lower end of the pressure or indicated thrust line between the 
lowest speed obtained on trial and the speed zero to be an unknown 
region, for which inferences can only be drawn from the portion of 
the pressure line above the lowest trial speed. But we are not in 
such complete ignorance of this portion of the pressure line or indi- 
cated thrust curve, since we know from Mr Froude's investigations 
that at these low speeds the resistance of the steamer is made up 
almost entirely of skin friction, and, further, that the power in 
which this resistance varies is pretty nearly the square of the 
speed. If it is true that, deducting the element of initial friction, 
the remaining elements in the gross power are practically propor- 
tional to the effective power, i.e., the product of ship's resistance 
and speed divided by 33,000, then it may be held that the curve of 
pressure or indicated thrust, less the amount due to initial friction, 
will follow in its form the curve due to the actual resistance of the 
steamer. In this case, we can with Mr Fronde complete the lower 
end of the resistance curve as a parabola. But if we do this we 
shall not obtain a straight line with Mr Mansel's system of logarithm 
mic off-setting, but a line which will have in it a contrary flexure^ 
and will finish against the vertical passing through the speed zero 
with a curve convex to the axis of speed. Mr Froude has shown 
this at length in the letter which he addressed to Mr Mansel. Mr 
Mansel cau hardly object to the idea that the indicated thrust or 



76 On Progressive Spefd Trials. 

pressure less that due to initial friction bears a fairly constant ratio 
to the resistance, because in his original analysis of power added to 
the discussion of my paper in 1875 he practically worked upon such 
a basis. 

I must now show that Mr ManseFs straight lines are exceptions 
and not the rule, and that, judged by such a body of experiments as 
I shaU lay before this Institution, they must be called haphazard 
coincidences. This proved, the whole fabric of his reasoning falls 
to pieces, being supported by nothing else than such coin- 
cidences. On the other hand, Mr Fronde's method remains 
founded upon an idea deduced from many experiments, and is there- 
fore of greater interest. I do not say of greater value, because I do 
not think it is possible either by Mr ManseFs or Mr Fronde's 
method to arrive at a quantitative measure of the initial friction. 
The variation of the results as shown by both these methods is 
sufficient to shake confidencein them, and the late Mr Fronde, who 
was eminently given to hold lightly to ideas which were not con- 
firmed by manifold experiments, had doubts upon his method which 
do not seem to have occurred to Mr Mansel with reference to his 
method. These are illustrated in the following quotations from 
letters of Mr Fronde addressed to me on 24th May and 4th Julyt 
1876, in which he was writing about the trials of H.M.S. '^ Shah." 
In the former he says—" As to the ' Shah ' we got what seemed 
piimd fade a very fair curve of power and pressures, but the 
particulars, when plotted, were, in the first place, somewhat incon- 
sistent with each other at the low speeds, and, in the second place, 
gave at all events a measure of the constant friction which was 
scarcely credible from its smallness*— one interpretation made it 
equivalent to only about ^ of the maximum working pressure, the 
other about ^. But at the higher speeds, interpreting the indicated 
thrusts by the ship's ascertained curve of resistance which our 
experiments here had supplied, it appeared that the working friction 
was excessively great, getting on for equivalent to, or even in excess 
of, the ship's true resistance at the respective high speeds." In the 
second letter he says—" The * Shah's ' constant friction does not 



On Progrestm Speed Trials, 77 

seem to be as much as ^ of the mazimam load; bat the lower speeds 
were not good. It seems hardly intelligible too — for one of the 
crank pins was continually heating." 

If you will refer to the table giving the comparative initial friction 
by Mr Froude's and Mr Mansel's methods from the list of selected 
progressive trials already described you will observe that the number 
of trials included in that table is 30. The whole of the power and 
speed curves of these trials have been reduced to curves of logarithms 
of indicated thrust, and out of their number only 12 can be said to 
approximate to straight lines. In order to show you how leniently 
these cases have been judged, Fig. 4, Plate YII., shows the best and 
worst of the 12 curves with reference to straightness. These are the 
trials corresponding to the first division of the initial friction table 
in the Appendix. In this division the straightness ranges from that 
of the " Goa " to the curvature of the " Quetta's " line. 

In Fig. 5, Plate VII., are given the indicated thrust lines correspond- 
ing to the second division of the initial friction table, lines which, 
although inferior in straightness to those in the first division, are 
such as to allow of their being, with some fairness, carried on to the 
speed zero for the purpose of defining the initial friction. In this 
division the '' Wairarapa" (2nd trial) represents the nearest approach 
to straightness, and the ''Booldana" the greatest departure from it 
In Fig. 6, Plate YII., is given the indicated thrust line of the *^ Clyde," 
which is one of the worst of the third division of the table. The 
lines in this division are so irregular in their curvature as to render 
them useless for the purposes of determining the initial friction 
ordinate. Of all the steamers enumerated in the table, the 
''Merkara," "Goa," and one other only have logarithmic lines 
which can really be called straight. As a matter of curiosity, I have 
given also a diagram of the trials of four vessels out of several built 
by my firm, of which Mr Mansel has at various times published the 
logarithmic lines. These four vessels have been selected because 
the five indicated thrust lines produced from their trials have not 
less than four trial spots each. On this diagram the ^^ Merkara " 

and ^ Goa," just mentioned, appear. 



78 On Pfogrmm Sfud Trials, 

But it is not alone by data^colleoted from the special records of 
my own firm that the exceptional nature of Mr Mansel's straight 
lines can be shown. If you will refer to Figs. 1, 2, and 8, Plate VI., 
you will find the results of the progressive trials of six Admiralty 
vessels plotted by Mr Mansel's method, some of the plottings having 
been previously published by Mr Mansel himself. Many of the lines 
are very far from straight, the best approximations being two lines 
for the ** Iris," one for the " Carysfort," and the one for the "Shah." 
These trials have also been selected on the ground of their having 
not less than four trial spots and complete immersion of the pro- 
peller. Fig. 1 shows the lines deduced from the " Carysf ort's *' 
trials, Fig. 2 those of the ''Prince Consort," the "Hecla," the 
" Heroine," and the « Shah," and Fig. 3 those of the « Iris." 

Again it is not only by progressive speed trials, in which, so far 
as the indicated horsepower is concerned, many variables are 
involved, that Mr Mansel's method can be shown to be inherently 
wrong. We have, thanks to the genius of Mr Froude, accurate 
methods of model experiments by which to judge such propositions, 
and their application to a very much wider range of speeds than is 
possible on the measured mile in all but very exceptional types of 
steamers. It is not difficult to show that Mr Mansel's method of 
straight lines is only applicable when the pressure or indicated 
thrust curves have no contrary flexure, but all experiment curves 
deduced from models have contrary flexures, and in steamers such 
as the torpedo boats, where the speed trials are carried far enough, 
the contrary flexures become apparent even in the indicated horse- 
power curves. The late Mr Froude, in his most interesting and 
valuable paper upon the effects of the addition of middle body to 
models, first indicated the causes of these contrary flexures or humps 
and hollows in the curves. 

These peculiarities, an example of which — taken from our own 
model results — is shown on Fig. 10, Plate X., exist in the resistance 
curves of aU models, and the first hump, which is only slightly 
defined, begins at speeds far below those proportioned to the very 
high speeds of the torpedo-boats : for example in the '^ Merkara," 



On Progresiive Speed Triab. 79 

the first hump which wehave been able to trace is at a speed for the 
ship below 13 knots. Faint indications of small humps existing 
even much below this rate of speed are sometimes traceable in 
resistance curves. As shown both by Mr Froude and his son, the 
positions of these humps and hollows on the resistance curves are 
determined by the varying positions of the two kinds and series of 
waves accompanying the model. But this is a subject far too large 
to be treated within the limits of this paper. Ample materials for 
its study and further development exist in their papers. They con- 
tain the results of their experiments and observations upon these' 
interesting points. In connection with this subject of waves it may 
interest you to see a comparison we have been able to make between 
the wave profiles of two of our paddle steamers — ^the "Minerva" 
and ^* Lucinda " — the latter tried only last. Saturday, as these wave 
profiles were observed upon the mile and as they were observed at 
the corresponding speed of the model in the experimental tank. The 
wave profiles are for two speeds in the one case and for one speed in 
the other, and their comparisons are shown in Fig. 1 1, Plate XL, and 
Fig. 12, Plate XII. These wave profiles were observed and plotted 
quite independently, and were traced to the same scale upon cor- 
responding profiles of the steamer. When the tracings were laid 
upon each other the result was as shown in the diagram. It will 
be observed that the profiles do not correspond abaft the paddle 
wheels, but this want of correspondence is easily accounted for by 
the effect of the paddle race upon the water surface. The corres- 
pondence between the wave raised by the model in the tank and 
that raised by the full-sized steamer on the mile, which is the basis 
of Mr Fronde's law of comparison, has a most useful bearing, in 
connection with our tank, upon the prediction of the speeds of fast 
paddle steamers. As the efficiency of the paddle wheel depends 
upon the proper immersion of its floats, it is evident, if the steamer 
is driven at a speed which causes a wave crest beneath the paddle 
wheel, there is a risk of the floats being over immersed. On the 
other hand, if the speed of the steamer causes a wave trough 
beneath the paddle wheel, there is a risk of the floats being insuf- 



80 A» ProgresiWi Speed Triabi 

ficiently immersed. A most interesting practical iOostration of this 
last condition was given at the 1881 meeting of the Institation of 
Naval Architects by one of the members of this Institution, Mr 
James Hamilton, jan. In the discussion following Mr Hamilton's 
paper Mr R. K Froude pointed out that the occurrence of a wave 
trough or wave crest beneath the paddle floats has a further im- 
portance from the fact that in the case of the crest coming beneath 
the wheel the floats will be working in a forward moving current, 
whereas in the case of a hollow they will be working in a stemward 
current As the humps on the resistance curves, to which I referred 
above, occur at comparatively moderate speeds, the measured mile 
trials of ordinary steamers, if the spots were sufficiently numerous, 
would very probably show irregularities which are at present unap. 
parent. In the only case known to me where very frequent spots 
have been obtained from the trial of a steamer such a hump and 
hollow are very distinctly shown. This trial was carried out on the 
'' Spartan " by Mr Biles, naval architect at the Clydebank Shipyard. 
The method of trial and the apparatus employed on the occasion we 
owe to his invention and energy. At the time Mr Biles read his 
paper upon this new method, I gave it a hearty welcome, upon the 
ground that it promised to link up much more closely the results of 
tank work and actual trials. I refer to the " Spartan " as a proof of 
the necessity which exists for progressive trials involving more 
frequent spots than are now common. For the speed at which they 
occur, the hump and hollow in her curve appear more pronounced 
than one would expect. 

In order to illustrate the effect of Mr Mansel's method upon 
model experiments, I have had the resistance curves of two models 
tried in our tank, which are in no way exceptional, plotted out in 
Fig. 7, Plate VII. The abscissae represent speed, and the ordinates 
the logarithms of the resistances of ships similar to the models at 
the various speeds. It will be seen from this diagram that there is 
not even an approach to straightness in these lines. 

With Mr ManseFs method of analysing the power developed in 
progressive trials by means of logarithmic straight lines, there are 



On, Progressive Speed Triab. 81 

four quantities which require to be determined before speed predic- 
tion can be attempted. 

L The amount of the initial friction. 

2. The zero ordinate of the revolution logarithmic line. 

3. The angle of the pressure logarithmic line ; and 

4. The angle of the revolution logarithmic line. 

Mr Mansel reduces these four items to two by working with the 
gross power line and its angle, but even for the use of this in pre- 
diction no guiding principles are laid down by him. 

I conceive it quite possible that from a sufficient amount of data 
the first two quantities could be assumed for any given new vessel 
with such a margin of allowance as to make them safe, but I have 
never yet been able to see on what principle Mr Mansel could select 
the angles of the two straight lines or of the one straight line, nor 
does he show in any of his papers how he would propose to do this 
or what he would make the test of these angles. He gives in the 
discussion on his paper *' On some points in the theory of thermo- 
dynamics" a rough general rule, but no guiding principles. In 
truth, one of the weaknesses of his method, apart altogether from 
its want of correspondence with large experience, is its comparative 
uselessness for purposes of prediction ; I am not aware of any naval 
architect who has so used it. Is this failure in the power of pre- 
diction not in itself ^corroborative proof of the error of the whole 
formula 't 

Mr Mansel, in at least two of his writings subsequent to March 

1876, found occasion to doubt the universality of the application of 

the laws of his straight lines. The most evident occasion for such 

doubts certainly exists in the torpedo boats. The humps and 

hollows apparent upon their power. and speed curves are sufficient 

to show that they are not likely to be reducible to sHraight lines. 

On this account Mr Mansel, in the paper last referred to, found 

himself obliged to resort to a series of articulated straight lines 

instead of the single straight line which he had been previously 

using. To show the general nature of the indicated thrust curve 

of the torpedo boats, and of the logarithmic line deduced therefrom, 

12 



82 On Progressive Speed Trials. 

I give one example in Fig. 9, Plate IX. This represents a boat built 
by Messrs Yarrow k Co., the trials of which were published in 
Engineering on the 17th October, 1879, and are, I believe, thoroughly 
trustworthy. Mr Yarrow informs me the screw was four inches oat 
of water when the boat was at rest, but was completely immersed 
when running. But the case of the torpedo boats does not differ 
from that of any other ordinary steamer, except that they have an 
exceptionally high allowance of power, and can consequently be 
driven at speeds which are impossible for the ordinary types. We 
know from our model experiments that steamers now running at 
speeds not exceeding ordinary expectations would, if supplied with 
power proportionate to that in the torpedo boats, perform as great 
feats, and show the same humps and hollows in their speed curves. 
Mr Mansel, in his note oh the trials of H.M.S. ''Iris," published in 
The Engineer^ 2i2nd March, 1878, also admits that a straight line 
does not adequately suit the case of the '^ Prince Consort/' although 
that ship IB not at all powered as the torpedo boats are powered. 
It is a very great pity that these side lights of doubt^ which met 
him in the way of his investigations, did not lead him to see that 
instead of the character of universality his method had only the 
character of occasional fitness. 

I notice that A(r Mansel speaks in many cases as if there were one 
speed suitable and proper for each steamer, and I am surprised to 
find him, in the present state of our knowledge, giving currency to 
such an idea. There is no single speed proper to any type of vessel, 
but if we are to judge from the resistance curves found by experi- 
ment from models there is a series of speeds indicated by the humps 
in these curves unfavourable, and another indicated by the hollows 
of these curves favourable, for easy propulsion. But these humps 
and hollows rather indicate groups of favourable and untavourable 
speeds than determine individual speeds. The changes in the curves 
are not of the nature of cliffs, as one would expect from the old 
notion of special speeds, but gentle undulations from hollow meadows 
to rounded hills. In speaking of favourable and unfavourable I am 
only doing so in a popular sense, because these conditions may be 



On Progressive Speed Trials, 83 

traversed by other consideratioiis which would lead one to choose, even 
after a carefal inVoBtigation, a " hump " instead of a " hollow " speed 
for particular purposes. Each model has these humps and hollows 
arranged and formed differently, and of different amounts, according 
to the variation of the proportions of its dimensions and the varia- 
tion of its fineness, and for each model, if perfect accuracy is desired 
in prediction at high rates of speed, such characteristics must be 
found by experiment. No doubt the notion of appropriate speeds 
peculiar to different types of steamers had some value in it as a 
stimulant to further inquiry, and we owe much to the late Mr John 
Scott Russell for its utility in this sense. But the notion has now 
ceased to be useful. Doubtless the fact that in some steamers tried 
progressively the power and speed curve tended to become vertical 
at the higher speeds somewhat revived- this old notion. But experi- 
ments and better knowledge have since taught us not to trust to the 
finality hinted at by such speed curves, but to believe in further 
possibility. The addition of more power, changing the propeller if 
necessary, would, I am certain, in all such cases produce still, higher 
speeds. In several of his papers Mr Mansel asserts that his logar- 
ithmic line of the pressures turns up when the steamer is overdriven, 
but this is an incomplete statement, owing to an incomplete 
appreciation of the nature of resistance curves. When a steamer is 
driven at exceptionally high rates of speed the logarithmic straight 
line will be found not merely to turn up but also to turn down 
from its angular direction, owing to the contrary flexure in the 
ordinary curve. 

I think it well to say a few words upon the analysis of power with 
which Mr Mansel nine and a half years ago started his discussion of 
my progressive trial data. In this analysis he divided the gross 
indicated horse-power as has been already described in the earlier 
portion of this paper. I may remind you that he divided the 
effective horse-power, E,, into : — E,, the power consumed in over- 
coming the surface friction of the vessel's hull ; E^ the power con- 
sumed in movements communicated to the water in the vicinity of 
the vessel ; and E,, a credit quantity for the power recovered by the 



84 On Progressive Speed Trials. 

propeller from the wake. At the speeds with which he was dealing 
he asserted that Em absorbed the larger portion of the effective horse- 
power. This is ap erroneous statement, and had ho carefully studied 
the late Mr Fronde's experimental work ia connection with the 
analysis of resistance he would have found the reverse to be the 
case, and that at the most of the speeds involved the skin Mction 
formed the largest portion of the resistance, as can be well seen on 
Fig. 10, Plate X. But Mr Mansel was unable to pursue this analysis 
further, because he had not the command of the necessary apparatus 
for experiments to carry out the investigation. 

In Mr Fronde's analysis of the expenditure of the indicated horse- 
power made in his paper upon this subject read before the Institu- 
tion of Naval Architects in 1876, he split up the indicated horse- 
power into two factors, the one being the ratio of the speed of the 
propeller to the speed of the ship, or what Mr Mansel calls the slip 
ratio, and the other an item to which Mr Froude gives the name 
Ship's Horse Power. This latter element he divides up into the 
following terms : — 

1. The effective horsepower corresponding to the resistance of 
the vessel if towed. 

2. The power spent on augmentation of the resistance due to the 
action of the propeller, which causes a suction on the run of the 
vessel, and consequent decrease of pressure favourable to her pro- 
pulsion. 

3. The power spent on friction of the propeller. 

4. The power spent on the initial friction of the machinery. 

5. The power spent on the friction of the load; and 
G. The power required for pump duty. 

In the course of his analysis, which he did not lay down as 
absolute, he recommended the reduction of the power term to a force 
term by converting it into indicated thrust, indicated thrust being 
the indicated horse-power multiplied by 33,000, and divided by the 
speed of the propeller in feet per minute. 3y the use of a multiplier, 
constant for any given steamer, this indicated thrust can be im- 
mediately reduced to Mr Mansel's term of P + rp. It will be 



On Progressive Speed Trials. 85 

noticed by any ono who reads Mr Fronde's paper carefully that he 
gave very grave prominence to the effect of the propeUer in aug- 
menting the resistance of the vessel, but he did not, in the course of 
his paper, make any mention of the help afforded the propeller by 
the wake. In Mr Mansel'^ analysis of power it is curions that while 
he takes no notice of the augmentation of resistance caused by the 
propeller, which is a discovery of Mr Fronde's — the result of experi- 
ment — he laid very considerable stress upon wliat he called the 
recovered power, i.e., the power recovered by the propeller from the 
wake. I understand Mr Froude summed up all such effects ih the 
item of slip, but he does not develop the matter, and in this connec- 
tion I think it right to draw attention to the prominence given to it 
by Mr Mansel. The series of tank experiments in which the propeller 
truck was added to the model resistance truck commenced by the 
late Mr Froude, and continued by his son, have led to some very 
curious information being obtained on this point. I believe Mr R. 
£. Froude looks upon the augmentation of resistance, or thrust 
deduction as he prefers to call it, and the gain obtained for the 
propeller by working in the wake, as quantities which very nearly 
balance each other, but which may even leave a remainder in favour 
of the steamer. Both father and son have worked very hard and 
very steadily at this question. It is one which has not yet reached 
a complete solution, nor will it reach even an approximation to 
complete solution without a great deal more work being expended 
upon it. Without the help of model experiments it would be 
impossible to take any steps in it with certainty. 

By means of these experiments, and by means of Mr Fronde's 
law of comparison, it is now possible to predict the amount of the 
resistance of any given steamer at any speed with a very fair degree 
of accuracy, excepting in cases where the form is such as to produce 
considerable eddy resistance. Mr Froude summed up the resistance 
due to the motion of a vessel in the water as being comp6sed of 
three elements : — Skin friction, the resistance due to the formation 
of waves, and the resistance due to the formation of eddies. 
In an ordinary well-formed steamer the resistance due to the 



86 On Progressive Speed Trials. 

formation of eddies is so small that it scarcely affects the total 
results. Assuming this to be the case, then, knowing the -law of 
resistance due to the formation of waves as it connects models and 
full-sized steamers, and knowing also the law in accordance with 
which the surface friction varies with fair approximation, we are 
able to predict the resistance of a full sized vessel, and to state the 
amount of indicated horsepower which would be required to drive 
that vessel at a given speed if the whole of the power developed in 
the engines were applied to this purpose without any loss. I may 
remark that the variation of the element of skin friction is not con- 
stant with increase of length, but decreases, as measured per unit of 
surface, with increase of absolute length of the surface. Mr Mansel 
uses a formula of Beaufoy's in which no allowance is made for this 
peculiarity of variation ; very probably it had not been observed in 
fieaufoy's time ; but it is of very vital importance to these investi- 
gations, as without it the prediction of the resistance of the full- 
sized vessel from the model experiments would be more hazardous. 
But the subject of the analysis of indicated horse-power, of which 
the vessel's resistance forms such an important part, is too large for 
treatment in this paper. I have, therefore, relegated to the appendix 
a few further remarks upon it, together with comparative diagrams 
showing with as much clearness as possible not only the methods of 
Mr Mansel and the late Mr Froude, but also the present condition 
of tffitt analysis. From what has gone befora, it is evident that it is 
only by means of experiment we can arrive at any really valuable 
information regarding power analysis, and I think it is much to be 
regretted that Mr Mansel, with his great ability, was so easily 
tempted away from this really promising side of the subject. There 
is an immense deal yet to be done in it by patient and careful experi- 
menters, and there is no reason why a man of Mr Mansel's ability 
should not have taken his share in such useful and pleasant work. 
Indeed, in the discussion upon my paper in April, 1875, he states 
on page 210, referring to the initial friction : — ^< The real value of 
this quantity in our ordinary direct-acting compound engines would 
be an important piece of information, which it is hoped some 



On Progrmm Speed Trials. 87 

engineering member may see his vray to experiment upon." In this 
sentence Mr Mansel points out the true method of investigation, and 
the only one whichr will be productive of valuable fruit Something 
also may be done to help forivard such investigations by more 
exhaustive methods of progressive trials, either in the way of obtain- 
ing many more spots of observation, or in the addition of Mr Biles' 
method to the ordinary measured mile trials. Further, if it is 
correct that the analysis of indicated horse-power is practically hope- 
less without some definite knowledge of the resistance of the vessel, 
it is apparent that without the help of an experimental tank real pro- 
gress in the direction of effective analysis is impossible. The only sub- 
stitute I know for tank experiments, but one useless for purposes of 
individual prediction, would be the towing of the full-sized steamers 
at the various speeds on the measured mile ; but excepting in rare 
cases the expense of such a method of investigation would be 
enormous, and beyond the financial powers of any individuals or 
firms, however willing thesQ individuals or firms might be to spend 
money upon such investigation. I am, therefore, convinced that 
experimental tanks will become common in the future. My own firm 
could very easily employ two tanks instead of one, and we are at 
the present moment by means of log propellers and ioiprovements in 
the towing machinery, attempting to increase the experimental out- 
put by at least 50 per cent. I do not believe a public experimental 
tank has much chance of success, for over and above the elements 
of jealousy and distrust, which would be pretty sure to enter into 

. its use, there is the difficulty that unless each individual can com- 
mand not only the special item of information he requires, but 
practically the resultant of all the information obtained in the tank, 

• the single itenr of information is of very little use to him. In this 
respect an experimental tank entirely differs from a chain-testing 
house, or such establishments for general testing purposes as are 
conducted by Mr Kirkaldy and Professor Kennedy. 

In conclusion, I would urge upon Mr Mansel not further to press 
his method, because, if accepted by any large portion of the practical 
world (which I hope it will not be) it would certainly have three 



88 On Progresiive Spied Trials. 

effects : — First, by the assumption that the pressure or resistance 
ordinates, set off logarithmically, will produce straight linesy to 
obscure the real need for many spots in progressive trials. What 
we want is more accurate and full progressive trials, and not less 
complete trials. Second, Mr Mansel's method, if accepted, would do 
liarm, by setting up a quite incorrect standard of accuracy for the 
results of trials. I have noticed in several of his papers he has 
pointed to variations from his straight line as indicating inaccuracies 
in the trials. The probability is that the variations indicate im^ 
portant changes rather than inaccuracies. Third, Mr Manael's 
method would do harm, as pointed out by Mr Froude in his very 
admirable letter which by Mr ManseFs courtesy I have had the 
opportunity of perusing, in the reduction of the scale of the ordinates 
produced by setting them off logarithmically tending to hide excep- 
tions and small differences, instead of defining them. I do not 
think it possible to put this view of the subject better than it is put 
by the late Mr Froude, and I believe np greater advantage could 
result to the Institution from this discussion than that Mr Mansel 
should be induced to print this letter in full in connection with it. 
Mr B. E. Froude has drawn my attention to another objection to 
the use of Mr JJIfansel's logarithmic straight lines, and it is this — 
that, while a logarithmic notation is convenient for quantities which 
have to be analysed into factors, it is unsuitable for quantities which 
have to be analysed into terms. But the analysis of I.H.P. into its 
various elements corresponding to the elements of resistance and 
also to the elements of loss is more an analysis of terms than an 
analysis of factors. Is it not possible that this very peculiarity of 
logarithmic notation, pointed out by Mr K. E. Froude, may have led 
Mr Mansel to abandon his original and more excellent method of. 
analysis, which was one of terms as well as of factors, for the more 
restricted and easier but less fruitful analysis of pressures and 
revolutions 1 I may here acknowledge my indebtedness to Mr R* 
E. Froude for his great kindness in many suggestions, and much 
valuable information afforded mc as to the latest steps in the 
analysis of indicated horse-power. 



On Progressive Speed Trials, 89 

If we look to the fature it is evident there lie before us the pos- 
sibilities of very extraordinary performances in speed. Both for 
purposes of war and for purposes of quick passenger traffic, speeds 
are now being required and thought of which a few years ago would 
have been deemed impossible and absurd. Besides, it is to be 
remarked that great hopes have been raised in the popular mind by 
the performances of the small sized torpedo boats, and it is not easy 
to make the ordinary public understand what a very wide interval 
divides the performances of the torpedo boats from even the fastest 
performances which have been lately attained by A^tlantic steamers. 
Those who know the realities and the difficulties of the speed and 
power question are aware that in the torpedo boats there is a develop- 
ment of power sufficient to carry them in many cases into the region 
beyond the humps of their resistance curves. And they know that 
in no case has this region of the resistance curve ever been approached 
by any of the fast full-sized steamers. We are not likely soon to 
see torpedo boat performances on a large scale, but short of this there 
may soon be very wonderful speeds attained at sea, and far beyond 
those attained at the present moment. Looking to all these pos- 
sibilities, it seems an absolute necessity that our ideas upon speed 
and power and the resistance question should be large and catholic, 
and not cramped by insufficient and empirical formulse. There is 
an immense deal in these questions still awaiting solution, and I 
have not found it possible in this paper to do more than touch in a 
general way upon some of the most important points. This may 
stimulate the minds of those interested in the subject to further 
investigations and study on their own account. There is ample 
material for such students in the papers of the late Mr Froude and 
his son, and there is much hope for the future. But we must not 
underrate the difficulties of the subject, nor expect to get any rapid 
or haphazard solution of them. Like all solutions worth obtaining, 
they must be sought with great labour, great patience, multiplied 
experiments, and a readiness to doubt upon every point which 

experiment and practice do not fully confirm. 

13 



I'O On Progressive Speed Trials. 

APPENDIX 

Comparative Tabulated Statements of Analysis of Indicated 
Horse-Power. 

In Tables Nos. II. and III. are given tabulated statements of 
power analysis ; viz., that with which Mr Mansel started in 1875, and 
the late Mr Froude's as explained by him in 1876. Comparing these 
two analyses, it will be found that Mr Mansel has four main factors — 
the slip ratio, the factor involving constant decrement of pressare, the 
factor for friction due to the working load, and E^ The last of these 
factors he divides into the three terms E, , E^, and E,, there being in 
all six root elements in his analysis. In Mr Froude's analysis there 
are two main factors, one for slip and the other for s.u.P , or ship's 
horse-power as he calls it, which he again divides into six main 
terms : — The power spent on the net resistance of the ship, E.H.P.; the 
power spent on the augmentation of resistance ; the power spent on 
the water friction of the screw ; the power spent on the constant 
friction of the engines ; the power spent on the working friction 
of the engines ; and the power spent on air pump resistance. 
Further, the first term, E.H.P., is divided into speed and resistance^ 
the latter being of three kinds — wave-making, eddy-making, and 
surface friction. There are thus in Mr Fronde's analysis nine root 
elements as compared with the six in Mr Mansel's. 

In Table No. IV. is given the present condition of the power 
analysis in so far as I have been able to gather it from the papers 
of Mr K. E. Froude, and from information which he has very kindly 
afforded me. It involves experiments in the tank with models of 
ship and screw propeller, taken both separately and in combination. 
The indicated horsepower is here split up into five main terms, 
which are : — ^The power spent on the constant friction of the engines 
and shafting; the power spent on the working friction of the 
engines ; the power spent on pump duty ; the power spent on the 
thrust block friction ; and the D.H.P., or dynamometer horse-power, 
as found by such an instrument as the late Mr Froude*s turbine 



On Progressive Speed Trials. 9l 

dynamometer, less the thrust block friction. This last term is sub- 
divided into three factors, the factor for hull efficiency, the factor 
for screw efficiency, and the effective horse power. To make this 
power analysis clearer, this subdivision is preceded by a grouping of 
the factors under the heads of screw items and hull item. The 
factor for hull efficiency and the factor for screw efficiency are 
bracketed together under the head of screw items, and the e,h.p. is 
named — in opposition to them — the hull item. The meaning of 
this is that the E.H.P., or hull item, is found from experiments upon 
the model alone without propeller. On the other hand the screw 
items involve the action of the propeller ; the factor for hull efficiency . 
being obtained from experiments combining the propeller and the 
model, and the factor for screw efficiency from experiments with the 
propeller alone. Two sub factors of the factor for hull efficiency are 
shown, viz., the factor involving augmentation of resistance due to the 
action of the propeller, and the factor involving gain due to the wake. 
The former is obtained as follows : knowing the net resistance of the 
model at any given speed without the propeller, the augmented 
resistance is found for that speed with the propeller working behind, 
the slip being so regalated as to cause delivery of a thrust equal to 
that augmented resistance ; the ratio of the augmented resistance 
to the net resistance of the model is the factor involving augmen- 
tation. The factor involving gain to the propeller due to the wake 
is the speed of the model divided by the same speed less speed of 
wake, the latter speed being found by the increased facility for 
obtaining thrust, which the wake gives to the screw when the model 
is in front. It will be seen that it is reasonable to call the combina- 
tion of these two factors the factor for hull efficiency although the 
screw is involved in both of them, because in both the screw is 
considered with reference to its connection with the hull. The two 
sub factors of the factor for screw efficiency — viz., that involving 
true slip, and that involving water friction of screw are factors which 
are due entirely to the action of the propeller clear of the hull. 
They are not' at present deduced separately, but are obtained con- 
jointly from experiments with the propeller alone in the following 



92- On ProgresHve Speed Trials. 

way s — At the speed t&nder oonBideration the propeller is drireii 
with varying amounts of slip, and the driving force and thrust 
measured for each; the forces are brought into comparison by 
the principle of virtual velocities, each force being multiplied by 
the movement made in the same unit of time, and the ratio of the 
two — le.i of the driving force to the thrust — taken. This ratio, 
when the thrust is that which is required, is the factor sought ; its 
value varies with the thrust obtained or with the slip which is 
required to give that thrust ; when the thrust is very small the ratio 
is very large ; as the thrust increases it falls to a minimum, and then 
again increases as the thrust continues to increase. The hull item or 
third factor composing the D.H.P. less power for thrust block friction, 
corresponds exactly to the E.H.P. of the late Mr Froude, and being 
reduced to a resistance term is split up as with him into surface 
friction, eddy-making, and wave making. The wave item of the 
resistance is further split up into two terms, one of the transverse, 
and the other of the diverging series ; these two series being capable 
of sub-division into bow and stern groups; although this further 
possible analysis may be omitted at the present stage of the question. 
In the last analysis the number of root elements will bs seen to 
be 11. It is to be noted that all these elements have not as yet 
been either fully defined or quantified, nor is it by any means 
certain that we are at the end of the statement of the items of the 
analysis. 

One lesson we should learn from these three tables is, that progress 
in power analysis means, in so far as our steps have yet led us, pro* 
gress into unsuspected difficulty, and not advance into facile solutions. 
The work which lies before the experimenter and investigator in power 
analysis is not easy, and its importance and difficulty should not bo 
underrated. Another lesson which we may learn from the study 
of these tabular statements of analysis is that the main element re- 
quired is the resistance of the vessel. This is the kernel of the 
analysis in each case, and must be known before any progress can bo 
made in it Hence the absolute necessity of model experiments in 
any attempt to elucidate this difficult question. Bound the element 



On Progressive Speed Triah. 93 

of the ship's resistance, or rather round that element -transformed 
into effective horse-power, gather all the other elements in the 
expenditure of the power. To say this indeed is only to say that 
the power to be expended depends on the work to be performed ; 
it agrees with the argument already set forth in the body of this 
paper, that the curve of power expenditure must, if carefully 
plotted from sufficiently exact observations, bear a close relation- 
ship to the curve of the vessel's effective horse-power. 

It may be asked, if the analysis of power is so difficult, how can 
the experimental tank be made useful for the prediction of the speed 
and power of any new type of steamer 1 It is fortunate that we do 
not need to wait until we have a complete solution of the power 
analysis difficulty before being able to make such prediction, and as 
it may be of interest to this Institution to know the method pursued 
in such predictions by my own firm, I give the following explana- 
tion : — "When the resistance of any model has been obtained, then by 
means of Mr Froude's law of comparison, and by means also of his 
method of proportioning the skin friction of the full-sized ship to 
the skin friction of the model, the resistance of the full-sized vessel 
in lbs. is approximately found. When this is known it is converted 
into effective horse- power by multiplying it by the speed of the 
vessel in feet per minute, and dividing by 33,000. To convert the 
effective horse power into indicated horse -power, it is necessary to 
use ratios which have been obtained from past measured mile trials 
and tank experiments. These ratios, in our experience, we have 
found to vary from 46 per cent, to 60 per cent, of the gross indicated 
horse-power. This may seem a large range of variation, but the 
extremities of it are accounted for by very exceptional cases, of 
which the causes are pretty well known. The real range of the 
ratios which we use for regular work is very moderate in extent and 
confirmed by a large amount of data. But here, too, there is an 
immense field for investigation which can only be explored by most 
careful experimental work directed to the examination of every 
possible cause of the loss of power that occurs. 



94 



On Progresmt Speed Tridb. 



Letter from Mr Man8el to Mr W. Denny. 

Slip Dock, Kelvinhaugh, 

Glasgow, 17th May, 1875. 
Dear Sir, 

I am proud to write that I have got the most import- 
ant and novel part of my formulas in a much better shape, and 1 
am sure you will be pleased with the very close results to experi- 
ment and consequences indicated. I wrote my last letter to you 
hurriedly, and I know I made mistakes in the recovered power 
formula. I hope you will be able to follow out the calculations now 
enclosed, by the aid of the explanatory sheets ; if not, I will very 
gladly go over them with you. I have condensed the calculation on 
one sheet, and briefly summarize results : — 



"GOA." 






No. L 


No. II. 


No, III. 






Em 


= 


648 


347 


101 






Ef 

Er 


= 


436 
—222 


246 
— 156 


81 Note. 
—44 


Calculated 


862 


438 


138 


than could 
well be 


Experimental 


E. 




869 


438 


139 


expected. 


Differences, 


— 7 





— 1 




" Africa." 


No. I. 


No. II. 


No. III. 






E„ 


= 


792 


475 


232 






E, 

Er 


■; 


534 
—265 


333 
— 259 


174 

— 147 


Note. 


Calculated 




= 


1061 


549 


259 


Also a very 
close result. 


Ezperimenta 


IE, 




1066 
-5 


541 


254 






+ 8 


+ 5 





The '* Africa " at first proved a regular bete wotV, and bothered me 
sadly. Of course, like most philosophers, I often neglect facts lying 



On Progressive Speed Trials, 



95 



under my nose, and go on a wild goose chase after explanation of 
difficulties, which after all are simply important elements seeking 
recognition in imperfect formulas. In the present case it -led me to 
a better appreciation and more suitable form for the important 
elements, draft aft and angle of trim : — 



" Hawea." 


No. I. 


No.IL No. III. 


No. IV. 




E„ 
E, 

Br 


= 406 
= 273 

= —a 


251 

176 

— 72 


144 
106 

-64 


37 Note. 
32 

1 ~ Abeurdlr cor- 

rect ; don't 


Calcalated 


= 673 


355 


186 


blame me. I 
52 could not help 


Experimental E^ 


= 673 


353 


186 


.» it. It is just 
3^ OS the figures 







■+2 








came out. 


"Taupo," 


No, I. 


No. II. 


No. III. 


No. IV. 


E„ = 


440 


233 




126 


27 


E, = 


285 


158 




91 


23 


E, = 


+ 142 










+ 215 


Calculated 


867 


391 




217 


265 


Expt. Ey = 


814 


890 




216 


68 




53 


1 




1 


197 



Here we have a most singular result. No recovered power in any 
case. No. I. shows instead a large extra expenditure, and in the 
same direction No. IV. shows a result which is simply monstrous ! 
The source of these inebriate figures 'from our previously steady- 
going formula, at the two extreme experiments, is not difficult to 
fathom. We have imported into the formula a quantity E^., which 
is the gross indicated power, with certain deductions for working 
engines and slip, which, whenever under or over valued, the excess 
being raised to the fifth power, is enormously magnified, and this 
forms an excellent means of arriving at the true value of friction and 
other losses involved in the difiference between E and E^, Thus, if 
in these two experiments we take instead of the calculated values 



06 On Progressive Speed IHak, 

7074 and 14*90 lbs., the effective pressures at 68*82 and 1216 lbs, 
respectively — no really serioas difference — our formulas would have 
yielded the following figures :— 





No. I. 


No, II. 


No. III. 


No. IV 


E„ = 


410 


233 


126 


27 


E, = 


285 


158 


91 


23 


Er = 


-i-67 








5 


Calculated 


792 


391 


217 


55 


Expt. Ey 


792 


890 


216 


55 



Now, here we have a pretty little problem : how does the pressure 
5 lbs., which seems to suit working the engines in all former experi- 
ments and the two middle ones of " Taupo/' require to be 6-92 lbs. 
at the high speed and 7*74 lbs. at the low speed f This requires 
some thinking over, but I daresay you will have quite enough in the 
accompanying papers* to occupy your attention for a few days. I 
assure you it has fully occupied my every spare moment for a few 
weeks. 

I remain, yours very truly, in haste, 

ROBT. Mansel. 



* These accompanying papers contain the arithmetical work by which the 
figures in the letter were obtained. 






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98 



On Progreuitt Speed Trials. 



I 

I 
I 



f 



i 



»0 

00 



f 

JOB 

I 




h s s 

I J J 11 






On Progretsive Speed Irials. 



99 



!2i 



5 




100 On Progressive Speed Trials. 

After the reading of the paper, 

Mr Mans£L said he would not attempt, at that time^ to answer 
Mr Denny's paper, the evening being too far spent. He would like, 
however, to notice one statement in the paper where Mr Denny 
says—-" I think it well to say a few words upon the analysis of 
power with which Mr Mansel, nine and a half years ago, started his 
discussion of my progressive trial data/' He thought Mr Denny 
was here assuming rather much credit to himself; since, long before 
the time referred to, he had worked at such matters. He held in 
his hand the original papers of calculations made in 1859, when the 
Koyal Mail paddle steam vessel '* Scotia " was being designed. The 
following table, exhibited to the meeting, included various cal- 
culated elements of the distribution of power in some large paddle 
vessels, as taken from those papers, and were such calculations as 
he had been in the habit of making for Messrs Napier & Sons, for 
nine years previously, say from 1850 ! 



On Progressive Speed Trials, 



101 





H.M.S. 




ItH.S. 


R.H.8. 


R.M.S. 


R.M.8. 




•Victo- 
ria and 


R.M.S. 
* Persia* 


•Perria,' 
at sea 


'Perria,' 
ataea 


■Shan- 
non' 


'Scotia.' 
Estimate 


Length at mid depth, 


Albert/ 


(Clyde). 
351-5 


Ught. 


load. 


(Clyde). 


before 
bailding 


300 


do. 


do. 


829-0 


362-5 


Breadth, - 


40-25 


44-75 


do. 


do. 


43-75 


470 


Draft, . 


13-75 


18-0 


18-8 


23-8 


17-0 


17-0 


Midarea,- 


435 


650 


688 


892 


610 


660 


Displacement, - 


2160 


4000 


4396 


5844 


3880 


4420 


Co-effict of fineness, 


•47 


•53 


• •• 


• •• 


-59 


•67 










estimate 


Indicated Power, 
Speed, 


2406 


4250 


3798 


3340 


2928 


4600 


16- 


16-4 


14-58 


n-29 


18-9 


15-5 


Slip per cent., - 


22-0 


23-3 


• •• 


• •• 


258 


230 


Calculated Distribution of Power. 


Displacing water, 


902 ; 1458 , 1311 


789 1 1000 


1500 


Fluid friction, - 


734 , 1200 


1071 


627 


850 


1300 


Working engines, 


860 • 620 


565 


487 


430 


670 


Slip, - . 


450 840 


711 


G26 


650 


880 


Excess for oblique 


feather- 






feather- 




action of float, 


ing 


132 


140 


801 


ing 


150 


2446 


4250 


8798 


3340 


2930 


4500 



As many of the members had not seen his Letter of Beclamation, he 
thought it ought to have been read before Mr Denny's paper to show 
what was the ground on which the latter proceeded. Mr Mansel pro- 
ceeded to read some quotations from his Letter, and eventually it 
was agreed, on the suggestion of Mr Denny, to print in the Trans- 
actions, both the Letter of Reclamation and Mr Fronde's letter to 
Mr Mansel, which are appended. 



LETTER OF RECLAMATION. 



To THE PREsroEirr and Council of the 
Institution of Engineers and Shipbuilders in Scotland. 

Gentlemen— 

I have saffered a wrong which I cannot submit to ; and, on 
full consideration, have come to the conclusion that you are the 
appropriate body to which my representation of the matter ought to 
be addressed. 

About a fortnight ago, by mere chance, I noticed, at page 178 of 
" Transactions of the Institution of Naval Architects, Vol. XVII." 
on the 7th April, 1876, when speaking in the discussion of a paper 
'< On the Ratio of Indicated to Effective Horse Power," &c., by the 
late Dr William Froude, Mr William Denny considered himself 
justified in making the following statements : — 

" I must really enter upon one point which I feel a little unpleasant 
to myself. I have the pleasure of the friendship of Mr Froude, and 
of another very able man, Mr Mansel, who is known to many of 
our scientific shipbuilders here. When Mr Froude discovered by 
his analysis the way in which it was possible to measure the initial 
friction, I remember having a conversation with my friend Mr 
Mansel, and I put it to him that Mr Froude had thoroughly 
explained the discrepancies of the ^ Hawea ' and ' Taupo ' trials by 
reducing them to indicated thrust. My friend Mr Mansel at the 
time did not seem to think that this had been attained. Shortly 
afterwards however he came to me, and I believe he had forgotten 
what I had said to him, but he had come upon the same idea, and 
he has worked out this idea in a very interesting way. You will 
perhaps excuse my making use of the black board to show you this, 
as it is a point which I am very anxious this Institution should 
clearly understand. Mr Froude has, and has alone, the priority for 
the discovery that the amount cf initial friction could be found 



[ 2 ] 103 

out from progreBsive trials, and it is perhaps the most interesting 
discovery which has been made with regard to speeds for a very long 
time. You will see that a different method of analysis has provided 
us with, although not an exact confirmation, yet a very close 
confirmation of what Mr Froude has said. Mr ManseFs method of 
analysing was this. You will suppose that these are two scaled 
arms at right angles of a diagram, similar in all respects to that of 
the ' Pachumba.' Upon the horizontal arm is set off in ordinary 
arithmetical notation the speeds 1, 2, 3, 4, 5 knots, or whatever 
they may be. Upon the vertical arm, not the indicated horse- 
power, but the mean piston pressures equivalent to the indicated 
thrust (the idea of which, as I tell you, Mr Mansel had unconsciously 
borrowed I believe from my suggestions about Mr Froude) are set 
off not in arithmetical but logarithmic notation. In fact, the 
principle of setting off this arm is the principle of Ounter's scale 
carried out in only one scale. Now if any gentleman would set off 
on the speed ordinates the amount of mean cylinder pressure or 
indicated thrusts according to the logarithmic scale already described, 
as Mr Froude has done in arithmetical notation, a very curious 
thing happens [tUt^trating on the black board]. Strangely enough, 
Mr Fronde's curve becomes a straight line. With regard to what 
Mr Mansel did, and I have the deepest respect for Mr Mansel, you 
must acknowledge his great ability in seeing that it was possible by 
this means to show what Mr Froude has also shown. By simply 
producing the straight line, and measuring its zero ordinate, he 
shows the amount of the initial friction of the engines. 

" Mr Froude : May I ask does that proceed on the assumption 
as to the law that governs the resistance 1 It must involve some 
such fundamental rule. 

<^Mr Dennv : I do not think Mr Mansel originally did more - 
than proceed on the notion I had given him of what you had done, 
and I believe he forgot all about where the notion came from, 
which is common enough for all of us to do. I have myself occa- 
sionally borrowed from my friends ; but, when I have been reminded 
of it, I have acknowledged it. although I could not say at the time 
where the idea came from. 

" Mr Froudk : I fully agree with that j but I merely wanted to 



104 [ 8 ] 

understand the principle on which that line comes out a straight 
line. 

" Mr D£NNY : I do not know the principle, but in every case this 
line has come out a straight line, with one exception. Allow me to 
say this, because it will be confirmatory of something Mr Froade 
will have to tell you in a second paper. In some of the ships — ^I 
think notably the * Merkara' — where the speed was for us high, 13 
knots, this last curve did not come out straight but turned up here ; 
showing you, at that point, something — which you will see after- 
wards, and which Mr Froude will explain to you fully — ^had 
happened. What I may call an augmented increase of resistance 
had taken place there, which of course must have been due to the 
form of the ship. I know I am taking up a great deal of time ; but 
you will acknowledge that, as to one part of this, it has been a duty 
forced upon me, and not a part of my own inclination." 

Which, concisely stated, amounts to : R. Mansel, taking advantage 
of a private communication to him of a discovery of Dr Froude, had 
devised another means of representing the same idea, and proffered 
it to Mr William Denny as his own discovery. 

It is further an implied claim for Dr Froude of a principle embodied 
in the paper, '* Propositions on the Motion of Steam Vessels," which, 
on the 21st of the preceding month, I bad read before your 
Institution, for which paper the Marine Engineering Medal of that 
year was afterwards awarded me. 

For eight years, during two of which I filled the honourable office 
of President of your Institution, a charge of dishonourable conduct 
has been recorded in the Transactions of a kindred institution, of 
which I was not then a member, and no opportunity of ofifering an 
explanation was given me when it was placed there ! 

Notification of the existence of this charge was never made knowti 
to me, or it should immediately have been replied to, and shown to 
be absurd. During the summer of 1876, 1 did hear that Mr Denny 
had said something in this strain, '' in London." I did not inquire 
where, and even had I known, I should have concluded that a sense 
of fair dealing, directed to a comparison of Dr Froude's paper with 
mine, would have ensured the alteration or suppression of the 



[ 4 ] 105 

objectiouable statements I now find in the foregoing report of the 
discussion. 

Mr Denny had been doing a great work for naval science ; he had 
known me but a few months, and I was not so weak as to seek to 
take notice of any impulsive statements he might have made. I 
trusted he would come to see that they were unfounded, and regret 
that he had been so hasty. I never, however, imagined his mis- 
understanding would have carried him so far as to necessitate a 
public proof of his having made himself ridiculous about a fallacy ! 
At all events, this was my idea. 

Mr Denny's mistake was the supposition that I agreed with 
Dr Froude ; who, had he been in life, was the person to whom I 
should have appealed in this matter. It is, however, fortunate that 
in a letter to me, dated 28rd September, 1876, Dr Froude has left 
his own views on record ; and this letter may be briefly referred to 
as illustrative of the sorioos difference between us, leading directly 
to the most conflicting views on far more important subjects than 
the one imagined by Mr Denny. I might have been all wrong in 
differing from Dr Froude, and yet have been perfectly honest : I 
had my own opinions, and knew both how to state and defend 
them. 

My recollection of this regretful affair is quite clear. In the 
summer of 1875, Mr Denny having sent me trial data of two sister 
ships, my simple and direct mode of investigation, then unpublished, 
showed the friction in one to be abnormally great, and I wrote 
suggesting inquiry into the engineering data; also, personally 
meeting Mr Denny's partner, Mr Walter Brock, in Helensburgh, 
put pointed inquiries as to whether there was not a possibility of 
some error with the indicator springs. Mr Brock described the 
care taken in testing these matters, and said there was nothing in 
his department to explain the discrepancy. Late in the autumn, 
after Mr Denny had been meeting Dr Froude in England, happen- 
ing to be in Dumbarton, I had a hurried interview with Mr Denny 
in a lane, when about to start for the train. Mr Denny informed 
me Dr Froude had explained the whole matter to him --it was 
simply friction ; by drawing a curve and its tangent, and continuing 

the curve to the axis, he got the friction. I at once knew what Dr 

15 



10« [ 5 ] 

Froude had done, and challenged the accuracy of the value thus 
obtained. Mr Denny was indignant that I should question Dr 
Froude's method; high words passed between us (a party in hearing 
jocularly shouted out, " I say, boys, don't fight "), and I left him 
with the significant statement, There is mare than friction; I can 
prove U. Mr Denny cannot have forgotten this, for he taxed me 
with it on our next meeting; no doubt expecting that I would 
resile from, what he considered, an absurd position. I object to the 
sentence, ''Mr Mansel, at the time, did not seem to think that this 
(initial friction) had been attained." Then, and after, attainment 
of the object by Dr Froude's method was denied ! 

I do not doubt that Mr Denny honestly believed that Dr Fronde's 
method and mine were alike at bottom, and gave the same result, 
and in this belief he repelled any explanation ; but I must openly 
protest against Mr Denny's mistaken notions being recorded as the 
measure of my knowledge, and the biassed judge of my honour. 
In the letter referred to, written by Dr Froude some months after, 
and with the advantages of study of my papers, and even a short 
personal interview, at page 19* we find, ''I will continue to work 
out in detail the differences which arise out of the two modes of 
treating the question, as they issue in reference to the case of the 
' Merkara,' which is one we have both investigated;" and at the 
foot of page 21,t states the results, " 7*39 is the pretoure due (by 
your method) to the constant friction, whereas by mine it is 10*04/' 

Dr Froude also shows that his curve of pressures cannot develop 
into a straight line, as was the case with my curve, and therefore 
argues I must be wrong. 

Mr Denny writes, ''In every case the curve develops into a 
straight line," noticing an exception, which his data does not justify, 
so that, on his own showing, Mr Denny credited Dr Froude with a 
method which Dr Froude distinctly repudiates. 

The matter under consideration was interesting in itself, and led 
to many very important issues. I shall endeavour to give a brief 
discussion of the chief features. Mr Denny's paper on the " Diffi. 
culties of Speed Calculation " was discussed, at the Institution of 

• See pn^e 126. See page 127. 



[ 6 ] 107 

Engineers and Shipboildera in Scodand^ in April, 1875. The old 
*' mid area " formula was taken by me as a basis, and, by some 
obvions modifications, I showed that it might be reduced to the 
formula in the looped figure. 

E - ^• 



II. V« = 




a formula which, in the case of progressive speed trials on the same 
ship, the quantities in the upper and lower loops being then constant, 
simi lifies, as is easily seen, into, 

III. V« = C(P + rp — 5). 

(This was figured on the same diagram as IL, but wa» not published 
in the discussion ) So far, three mechanical principles are involved. 

First, Mechanical effects are only properly judged when referred 
to the powers producing tbem. (Smeaton's principle.) 

Second, Like kinds of mechanical effects are in constant ratio 
to the respective powers producing them. (Theory of the 
Admiralty co-efficients.) 

Third, When power is developed, and producing mechanical 
effect, the manifested pressure has a constant decrement 
which is independent of the velocity with which the effect 
is produced. (This decrement is known as Morin's con- 
stant) 



108 



[7 



Let us now refer to the data of the " Merkara," as fiimiBhed b j 
Mr Denny. 

S.S. "Merkara." 



Speed. 


Co-efficient. 


Preasare, 
(P ■» T>). 


12-91 

11-09 

9 20 

6-20 


579-4 
585-2 
551-0 
417-6 


78-30 
53-55 
38-12 
22-79 



On subfitituting these data in III.^ replacing the assumed special 
value 5 of Morin's constant by the general value m, we obviously 
get four equations^ 



IV. 



12 912 = 0(73-30— m). 
11-09- =C (53-55 — m). 

9-20« = C (38-12 — m). 

6-20« =^C (22-79— m). 

Now, if the investigation was free from error, by the third principle 
we should have the same value of m in all. To try this, we have to 
get rid of the common factor C, which is easiest done by dividing the 
members of the first equation by those of the second, those of the 
second equation by those of the third, &c.j and by transposition we 
thus get : 

73.30 — 53-55 



First and second, 



m = 53-55 — 



/12-91\»_ 
\1109/ 



Second and third, 



5 3-55 — 38-12 
m = 3812— /1109\* ^ 



Third and fourth, 



m = 22-79 — 



-/ 1109 V 
V9-20/ 

8 8-12—22-79 

V6-2U/ 



: — 2 09. 



= 406. 



= 10-04. 



Dr Froude's method of finding this quantity (the initial friction* 
as he supposed) was not to take his published method of the 



[ 8 ] 109 

indicated thrust curve, and the geometrical construction at the 
origin, as given in his paper of April, 1876, about which Mr Denny 
and I differed. Dr Froude wrote (page 9), " The algebraical mode 
is more definite, and may be relied on as accurate, if we have reason 
to believe that the resistance has not sensibly outrun the square of 
the speed." In effect, Dr Froude simply takes the two last of the 
foregoing four equations, and works out the value 10-04, which he 
assumes to be the true value of the " initial friction." 

But in this Dr Froude simply legs the guestion, for he had no 
more right to assume this value, than the 4-06 of the pair above, 
and the obviously absurd — 209 of the upper pair. It is true, a 
limitation is laid down that " the resistance is not to outrun the 
square of the speed," which amounts to saying that the method 
is not applicable to a steam vessel at all ; for I not only deny, 
but can offer most satisfactory proofs that in no instance does this 
assumed law, of resistance varying as the square of the speed, hold 
good ! This is a matter of paramount importance, and can best be 
approached by consideration of the relation between the second 

MV* 

principle and the quantity "^^ — , when derived from the progressive 

speed trials on a steam ship. The numerator represents the 

mechanical effect, the denominator the power doing it, and by the 

mechanical principle these should have a constant ratio. The fact 

is uniformly impressed upon us, that it is not so, and the reason is, 

that the numerator involves the V* hypothesis, assumed as a law, 

and the mechanical principle is quite obscured until the V^ is 

removed, and something much nearer the truth is put into its place. 

Take, for example, the "Merkara's" co-efficients, and multiply 

, ,, ^ ^. r . Log- ^0735 7 ,.,.,, T 

each of them by the factor — - — y^ , which is the process I 

have indicated, the V=^ denominator removing the V* influence from 
the co-efficient. The calculation is simple, and as follows : — 



110 



[M 



Speeds, - - 
Co^dente, • 


12-91 
579-4 


1109 
585-2 


9-20 
5510 


6-20 
417-0 ' 


Log co-efficiento, 
Add value -0735 V, 
Subtract Log V«, 

Log«, 


2-7G30 

•9489 

2-2218 


2 7673 

•8152 

2-0898 


2-7412 

-6762 

1-9276 

1-4898 


26207 : 
-4557 i 
1-6848 


1-4901 


1-4927 


1-4916 


Constant Batio, 


30-92 


3110 


80-89 


31-02 j 



This vindicates the second principle, and indicates the V* hypothesis, 
throughout the range of experiment in the ^' Merkara," to be an utter 
fallacy : for these new ratios are as nearly constant as the nature of 
the problem could lead us to expect That this is not an exceptional 
case, is best shown by giving the results of three more vessels, in 
which the fallacy of the V*^ hypothesis is -even more clearly shown. 



H.M.S. "Shah," 


H.M.8. "Iris," 


"Charlea Quint," 


j,^,^Log-;0792J 


Factor, I-«-;^f«?V 


Factor, Ji28-;;''8«V 


Speed. 


Co-eflU. 


Batio. 


Speed. 


Co-eflU. 


Batio. 


Speed. 


Co-eSta. 


Bado. 


16-45 


587-3 


43-58 


18-59 


594-9 


4270 


16-11 


702-8 


57-21 


1213 


702-4 


43-60 


15-75 


6905 


42-39 


13-42 


770-4 


57-33 ! 


8-01 


656-8 


44-10 


12-48 


770 


4iS-72 


9-82 


823-4 


57-30 


5-32 


466-9 


43 53 


8-32 


676-7 


41-12 






1 



In every case, multiplying the co-efficients by a factor of this same 
form, gives a ratio, constant in the same vessel, so long as the con- 
ditions other than power and speed remain the same. The inference 
from all this is irresistible, there is no proof whatever that V^ is the 
law of the resistance in a steam vessel Every formula in which 
this assumption is involved thereby becomes contradictory, both to 
facts and mechanical principles, and worse than of no value : it 
becomes misleading ! 

The correction of equations lY., so as to remove the original sin 
due to the V hypothesis in the Admiralty co-efficient^ from which 
ic was derived, and thus vindicate the third mechanical principle, 



[10] 



111 



is not difficult. We have simply to replace the first member V^ by 
the quantity, (1 + aV) b Log -* aV, Only, it may be noticed, the 
formula is very sensitive, and some collateral influences have to be 
allowed for to remove resulting variations in m. (See equation (d), 
sequel) The contrast of Dr Froude's method and mine, however, 
is more readily seen, as Dr Froude has shown, by taking his formula 
for the curve of pressures, which he writes, P » a + b Y' and 
from the data of the 9*2 and 6*2 knot trials calculates, a = 10*04 
and b = '3318, so that, 

(P + rp), or, as he writes, P = 10*04 + -3318 V«. 

At page 26, the calculated values by this formula are given up to 
10 knots, and in another column, the values derived by Dr Froude 
from my method, as follows ;— 

Ordinates of Curve of Pressures. 



SpMd*. 


Dr Fronde's Cunrew 


Logarithmic Mode. 





1004 


7-39 


1 


10-37 


8-86 


2 


11-87 


10-63 


8 


13-08 


12-75 


4 


15-35 


15-29 


5 


18-38 


18-38 


6 


21-98 


21-99 


8 


81-27 


81-68 


10 


48-22 


45*55 



But my reading of the " Merkara ' data is, in the general formula, 
P + rp = f Log -^ a V. We have f « 7*745, and a ^ 0756. 
The formula for the "Merkara," is, 

(P + rp) = 7-745 Log -^ -0756 V. 

As an example of the extreme simplicity and accuracy of this 
formula, the full calculation of the values for the trial, and a few 
assumed speeds, is as follows :— 



112 [ 11 ] 

Ordinfttes of Pressure Curve of " Merkara." 



Speeds, 


12«91 


1109 


9-20 


6-20 1 3-00 1-00 


•00 


Value, 0756 V, 
Log 7-745, - 

Sum, or 
Logs (P + rp), 


•9760 
•8890 


•8384 
•8890 


•6955 
-8890 


•4687 -2208, 0756 

-8890 -8890-8890 

1 1 


•0000; 
-88901 

1 


18650 


17274 


1-5845 


1 -357711 -llSSl -9646 


•8890 


By formula, - 
„ trial, 
„ Dr F.'s cunrei 


73-30 
7330 
65 34 


53-39 
53-55 
50-84 


•38-42 22-7& 1 130(5 ! 9-22 
38-12 22-79 ? | t 
8812 22-79 ' 1303 10-37 


7-745 

t 
1004 

1 



Here, the formula values are contrast^xl with the experimental 
and Dr Froade's values in the succeeding lines. It is obvious, from 
13 knots to 3, according to Dr Froude's figures for this last speed, 
there is as perfect agreement as could be expected between the 
formula values and the experimental. Now, from its nature, this 
curve of mine must develop into a straight line when the logarithmic 
ordinates are set up to the speed abscissas, and upon no reasonable 
principle can it be contended that the law giving a straight line 
from 13 to 3 knots should not continue true for the remaining 3 
knots: and thus by going to the origin we get the value of m 
belonging to the limits of experience. It is, however, a matter of 
certainty that experiments made between the 6-2 knot speed 
and zero, would liave shown a change of value of m, due to 
changed circumstances explained as the lower conjugaU solution. 
The value 10*04, however, being derived from the 9*2 and G*2 
knot speeds, is not in any way connected with the unknown 
region under the 6*2 speed, and consequently is neither true for the 
experimental nor the unknown lower speeds with the steam vessel. 
Dr Froude's curve is hopelessly erroneous at the higher speeds, 
and is only true for the 9*2 and 6-2 speeds, because he com- 
pelled it to take the true values at these points Let us now 

** Had this speed been given 9 '16 instead of 9-20, the value would have 
been 38*14, but the whole data indicates this speed to be 9*10 only, giving 
(P + rp) - 37*76, which is increased to 3812, by the simultaneous reduction 
of the revolutions from 45*07 to 44*75, the observed value; the pressures vary* 
iug inversely as the revolutions. 



[12] 113 

take formula III , and substituting for 5 the general value m, and 
for (P + rp), the equivalent general value f Log — ^ aV, we have, 

V2 = C (P + rp — 5). 

V2 = C(fLog-iaV— m), 
which, at the limit when V = 0, gives, 

= C(fLog-i — m), 
and consequently f = m, since Log - » = 1. 

Now, in the four equations of IV., whenever V has any definite 
value, the mechanical principle is violated; since, as shown, we 
have a variety of values of m, with nothing but empirical guessing 
to determine which is the right one. The reason is, the form V of 
the first member is a fallacy, and only when the V has no value, 
vanishing with the first member, does the second member indicate 
its involved truth that f = m, showing the origin ordinate of the 
curve to be the value of Morin's constant ; which, in virtue of the 
third principle, continues uniform through all the successive values 
ofV. 

Dr Fronde's explanations, given at page 27 of his letter, • are as 
follows: "The curve calculated by the equation P = a+bV*^, cuts 
exactly the two points of pressure given by the * Merkara ' experi- 
ments, for the 2 knots and the 9*2 knots. This, of course, it was 
bound to do, because it was calculated from them ; it, however, cats 
below the point which belongs to the 11*09 speed, and still more 
below that which belongs to the 12-91 speed. . . The meaning 
of all this is that, as a matter of fact, the resistance of the ^Merkara' 
is practically as the square of the speed, up to quite 9 knots, above 
this speed, the resistance increases in a higher ratio, and then of 
course for higher speeds deviates from the parabola, which correctly 
expresses it so far ; on the other hand, the line which is defined by 
the logarithms of the pressures is not absolutely straight, though 
it is nearly so, and when an absolutely straight line is substituted 
for it, and the pressures are calculated backwards from the ordinates 
of the .straight line, the resulting pressures are far more different 
from the true pressures than the logarithmic line is from the 

• See paj^e 130, 
16 



114 \\S] 

auumed straight line, and definite tangible error is thus introdaced 
into the data. Nevertheless, it happens that the series of pressures 
which are thns obtained from the straight line, indicates a resistance 
which grows more rapidly than as the square, and which thus has a 
rough sort of agreement with the real growth ; only the agreement 
is arbitrary and haphazard, and has no real relation with the special 
law of pressures which each form of ship requires (a law which is 
materially different for different forms), and will certainly contradict 
the law for almost any possible form of ship as the speed increases." 
There is nothing in this to bridge the interval between Dr Froude 
and me, or invalidate the strong reasons upon which I have chal- 
lenged the very basis of Dr Froude's speculations. I will in conclusion 
quote from' my letter in reply, to show the attitude taken by me at 
that time to be the same as now. The origin of this correspondence 
may be explained. I had one short and only interview with 
Dr Froude, at the Glasgow meeting of the British Association, in 
September, 1876. He had a printed copy of the first part of a 
paper I read two days after, and began to discuss some points 
which he thought erroneous. Shortly after I had a letter in which, 
after regretting that a sudden call to the south had prevented him 
from being present at the reading and discussion of my paper, 
resuming the discussion, he at much length proceeded to strengthen 
his position, and show forth the weakness of mine. My answer 
shows that, in my opinion, he had effected neither; and, omitting 
some trivial matters, began as follows : — 

Leiiei' to Dr Froude, 

« 9th October, 187G. 
" William Froude, Esq., LL.D., F.R.S. 

'* Dear Sir, — Your valued communication came to hand in due 

course, and I am much obliged and gratified by the great amount of 

trouble you have taken in order to explain your views on certain 

points of the difficult and important problem which, I believe, 

for a long course of years, has been a study for both you 'and me 

Doubtless there are several points on which, like sensible men, we 

may agree to difftr, without, in the least, impairing the good under- 



[14] 115 

standing and mutual respect which ought to characterise the 
discussion of any subject, and in an especial degree the discussion 
of a purely scientific one. . . As to the transactions, Section G, 
B. A. : you lost very little by being called away. My paper was 
set down last for Monday, and a Council meeting coming on at 
three o'clock, I think about twenty minutes was the time in which 
it was to be read and discussed. When about one third through I 
had to stop, . . . discussion there was none. Mr Denny described 
your mode of continuing the pressure curve to the origin ordinate, 
but, I thought, in a way that would lead a stranger to suppose we 
had arrived at precisely the same result, and had time permitted I 
would have noticed the points of difference. 

•** My paper opens with a declaration of its object—* the 
application of certain propositions to the experimental trials 
of steam vessels,' ... Hhe propositions are the state- 
ment of these experimental laws in this way exhibited and 
tested within the limits of experience.' I might simply chal- 
lenge the production of actual trials of steam vessels inconsistent 
witli these propositions, and might also assert * known dynamical 
data of the case' to lie between the least and greatest experimental 
speeds of these steam vessels, declining to be judged by data drawn 
from unknoicn seas at and about the origin. . . . However, I gladly 
waive all this, and beg to offer the following reply to your objections, 
'' A steam vessel is a machine in which power is developed to do 
work, and is subject to the same laws as other machines. Now, a 
machine in motion developing power has a constant deduction 
from the acting pressure which is independent of the velocity of 
its motion. I have denoted this defect of pressure by the symbol f, 
and, at page 4, you will notice I affirm that this quantity is not the 
measure of the moving friction alone, but this friction, in most 
cases, very much modified by external circumstances, of which, 
except by the resultant effect, we possess no definite measure. 

" To determine this resultant effect of the whole. I affirm two 
experiments at moderate speeds are alone necessary, and that the 
straight line drawn through the logarithms of the gross pressures. 



116 [15] 

set up as ordinates to the trial speeds as abscisssB, cuts off from the 
origin ordinate a line representing in like manner the logarithm of 
the quantity f* Pardon me for observing that in challenging this 
you labour under the disadvantage of not knowing the real ground 
of this assertion, which would have been more obvious if you had 
my paper in full before you. I send you the rough proof slips of the 
part immediately following. . . . 

" Allow me to indicate my propositions in a concise and sym- 
metrical form. 

" First, The logarilhrns of the gross presmres increase, from the 
value Log f at the origin, by the product of the speed and 
a constant factor a ; or, 

Log (P + rp)= aV -h Log f. 
*• Second, The logarithms of the number of revolutions per mile of 
the propeller, increase, from the value Log n^ at the origin, 
by the product of the speed and a constant factor P; or,. 

N 
Logy = ^V + Log no. 

'< Fourth, The logarithms of the ratio of effective pressure to the 

speed increase, ttom the value Log-p at the origin, by the 

product of the speed and a constant factor (^ + y) : or, 

'* The third proposition being a mere corollary of the two first, is 
left out of consideration, and my argument is : these propositions 
are not independent, but are conjointly satisfied by conditions which 
exist in a steam vessel, and express the mechanical principles 
involved in its direct motion. We may take one of these equations 
and put in any arbitrary values we please, but what sort of a steam 
vessel would answer to these suppositions ? Would it be ^ such as 
are designed and constructed by competent parties?' I submit that 
arguments founded on abstract and paitial considerations of num- 
bers have no force whatever, and, supposing we cannot agree upon 
principles between the origin and lower limits of observation, does 
it much matter 1 The question : do the propositions fairly interpret 



[16] 



117 



the phenomena between the limite of observation 1 is surely of vastly 
greater importance. 

'^ In my remarks I have stated two speeds only as being requisite ; 
this involves their being fairly accurate, which many are not ; hence 
the virtue of Mr Denny's more numerous observations, enabling us 
to get a fairer average of the two for calculation purposes." 

Finally: in justification of my views ou the whole matter, and in 
illustration of their perfect agreement with the facts of experience, 
I add the results of their application to this special vessel the 
" Merkara," in respect of the Power, Bevolutions, Piston Pressures, 
and Residual Pressures. The values of these elements being cal- 
culated by the following formulas, are contrasted with the values 
given or involved in Mr Denny's data for this vessel. 

"Merkara*' 
Power, E =16-90 V Log -^ -0735 V. (a) 

Revolutions, N = 5-176 V Log-i--0021 V. (b) 

Piston Pressures, P + rp = 7-745 Log-^ -0756 V. (c) 

Residual Pressures, P + rp — 7-745 = 1226 V Log-^ -0478 V. (d) 
Calculated Results. 



Trial 
Speeils. 


Power. 


BeTolutioDs. 


Piston PreasoTCs. 


Reudaal Pres'res. 


Trial. 


Form.(a) 


Trial. Fonn.(b) 


TriaL 

73-30 
53-55 
3812 
22-79 


Fonn.(c) 


Trial. 


Fonn (d) 

66-555 
46-09 
30-38 
15045 


12-91 

1109 

•910 

C-20 


1948 

1225 

718 

299 


1940 

1225 

718 

299 


63-23 
54-35 
44-75 
3115 


62-78 
54-40 
45-07 
31-15 


73-80 
53-89 
37-76 
22-79 


65-556 
45-805 
30-375 
15-045 



ROBERT MANSEL, 



Whiteinch, Glasgow, 2lBt April, 1884. 



♦ The speed given by Mr Benny for this experiment is 9*20 knots, but the 
results indicate 9'10 as the more probable value. This trial also illastrates 
the interchange of revolutions and pressure, so that witli the power following 
the normal law, the revolutions and pressures, viewed separately, seem to 
depart from their normal law. 



lis On Progressive Speed Trials. 

Letter fr(m Dr Fraude to Mr Bobert Hansel 

Chelston Cross, Torquay, 23rd September, 1876. 

Dear Sir, — I was much obliged for the corrected copies of your 
paper of " Propositions on the Direct Motion of Steam Vessels " 
which you were so good as to send me at Sir W. Thomson's, and I 
regretted greatly that I was cut off from the opportunity of hearing 
the paper read and joining in the discussion, by being summoned 
(prematurely as it proved) to superintend some experiments at 
Portsmouth for the Admiralty. The experiments will not, in fact, 
take place till next week. 

I have not heard whether your paper was, in fact, read and dis- 
cussed. Had I been able to join in the discussion, I should have 
had to express my regret, that while in many respects I went along 
with you, that is, that my independent investigations had brought 
my ideas into pretty nearly the same course as yours, there were 
some very definite and not unimportant differences between us both 
in the mode of treating the data before us and in the conclusions 
arrived at. 

I have no wish to run into a controversial discussion, but as yoa 
have given me an opportunity of understanding your views better 
than I have done before, I should like in return to explain to you at 
least the most fundamental of the grounds of difference between us. 

Perhaps the first remark I shall have to make will seem to imply 
that I forget the saying which, I think, has a real force when applied 
to modes of scientific investigation, as to the circumstance to which 
it primarily belongs—** Each glazier can best use his own diamond." 
(By the way the improved method of mounting diamonds has greatly 
invalidated the original force of the saying.) No doubt each mind 
has its own grooves of thought in which it works best, and if it did 
not seem to me that your mode of handling Mr Denny's data had led 
you into an erroneous conclusion, I should have felt you were but 
workiug in your own groove, and I should not have felt entitled to 
say that by laying down — not the pressures themselves, but the 
logarithms on the speed abscissae — ^the real significance of the record 
was obscured, for if the step had not led you into error I should 



On Piogressive Speed Tiiais, 119 

have been bound to believe that your own method fitted your own 
groove of thought best. 

To me certainly the " logarithm of a pressure " conveys a less 
instructive meaning than the ** pressure" itself, and though no 
doubt on finding that the series of logarithmic ordinates resulted iu 
nearly a straight line, there must have been a fascination and a 
temptation to regard the line as probably straight up to the origin, 
and to assume this as a fact, I should myself have felt it dangerous 
to make the assumption, unless it in all respects rationally fitted the 
known underlying dynamical data of the case. Now these are 
certainly more readily associated with the " pressures " themselves 
than with their " logarithms," and to turn the former into the latter, 
seems to me only to obscure what is naturally clear. 

When I received Mr Denny's data from him, more than a year 
ago, the first thing I did was to use the pressures as ordinates to 
speed abscissa), and on doing so the result obviously at once, not 
only indicated the existence of the ^'constant" element of the 
engine friction, but suggested what is, to my mind at least, the true 
mode of determining its actual value, in virtue of the natural and 
obvious dynamic conditions on which the total pressures must depend. 

Before putting the results into actual figures T will explain my 
meaning by sketches. 



9 



II 



o 

g 



i I i I I 

Speed in knots. 



120 On Progressive Speed Trials. 

Laying off the piston pressures simply and nakedly, the four spots 
arranged themselves about as sketched. The arrangement was such 
as to make it quite clear they belonged to a curve which would not 
come down to the zero of pressure at the zero of speed. And the 
question which at once presented itself was, How would the curve 
have been continued if the ship could have been run at slower and 
slower speeds down to zero ? and again, What is the meaning of the 
curve not running down to zero 1 

The answer to the latter branch of the question supplied the 
answer to the first branch also. 

Obviously the meaning of this feature in the curve was, that it 
indicated that element of engine friction which may be called con- 
stant, being due to the dead weight of the working parts, and 
to the tightness of the piston packings, &c., elements of friction 
which may be regarded as practically constant ; while, of course, 
there must also be another element of friction, due to the stresses 
which constitute the working load, being the fruit of the ship s 
resistance, which grows greater as the load increases. 

We (you and I) are agreed here in principle, but as will be seen 
our modes of determining the constant friction load to results differ- 
ing in amount, and I am not without hope that I shall convince you 
that my method is the correct one. 

Bearing in mind the nature of the two causes of or demands fur 
piston pressure —(1) the constant friction; (2) the load due to the 
ship's resistance and its derivatives — it must be approximately true, 
especially at low speeds, that the total residue of piston pressure, 
after deducting the constant friction, will be proportionate to the 
ship's resistance at each speed. 

Moreover, we know quite well, and I believe you will agree with 
me here, that, at low speeds at all events, the ship's resistance is 
almost exactly as the square of her speed. 

If this be so, it follows that, at all moderate speeds, the piston 
pressure may be expressed by an equation of the form, 

P (or P + rp as you write it) = a + bv^, 
and the completion of the curve to the speed zero is accomplished 



On Progressive Speed Trials. 



121 



by the easy process of constructing the parabola which this equation 
represents. This may be done in two ways, one geometrical, the 
other algebraical 




(1) Geometrically. Draw a fair curve through the four spots, and 
draw its tangent, A A', through point 4. Then draw 6 B' (parallel 
to the speed-base) so as to cut A A' halfway between i>oint 4 and 
the speed zero. Then the line B B' will be the tangent to the 
parabola at the vertex and BO is (to scale) the pressure which 
corresponds with the constant friction. 

(2) The algebraic mode is more definite, and may be relied on as 
accurate if we have reason to believe that the resistance has not 
sensibly outrun the square of the speed at the speed belonging to 
point 3. If we are satisfied of this, the completion of the parabola 
is at once obtained by solving the following quadratic, 

. if oO, 4O, and 3O be the parabolic ordinates, at the origin, at 

point 4 and point 3 respectively, 

^0=00 + M* 3O = oO + b^v^ 

by which equations ^0 and b are readily determined ; and observe 

qO is the same as (a) in the equation to the parabola which I gave 

jast now. 

I proceed to explain why I think that your method of treating the 

ordinates — namely, laying off their logarithms as the basis of the 

17 



122 On Frogressm Speed Triah. 

determination — is in several ways misleading; and how, by adopt- 
ing it, you have erroneously estimated the constant friction. 

It is misleading because, as v increases, and the pressure ordinates 
increase to comparatively large figures, a given alteration of pres- 
sure ordinate produces a less and less alteration in the corresponding 
logarithmic ordinate, as indeed is obvious when one recollects the 
well-known differential expression, 

dy 

The greater y is, the less is dlogy for a given value of dy, and 
hence large and instructive features of the curvatures in the pressure 
curve vanish in the curve given by the logarithms of the pressure, 
and the resulting curve becomes more and more temptingly Uke a 
straight line. 

This tempting resemblance to a straight line has led you — / 
would say has misled you --into supposing that the same degree of 
straightness would be continued to the origin. The supposition is 
entirely gratuitous. The line could only continue straight in virtue 
of the existence of a very peculiar law of pressures near the origin — 
a law of pressures which we have not the slightest reason to suppose 
can exist. And on the other hand, if we suppose the law of the 
pressures to be such as we know it must be with a very dose appro- 
ximation ; that is to say, if we assume the pressure, in the region of 
moderate speeds, to be defined by the equation P = a ^ to^, it is 
easy to prove that the line given by the logarithmic ordinates is not 
straight down to the origin, but curved so as to cut the vertical axis 
at right angles. 

If, for instance, we assume that A A', or the line of logarithmic 
ordinates, continues to run straight right down to the origin, then 
(it is easily proved) the curve of pressures will cut the vertical axis 
obliquely as sketched; which we know cannot be true ; or if the 
curve of pressures be described by an equation of the form F=a+bv'*, 
then the tangent to the logarithmic curve will, at the origin, be 
horizontal, as sketched. (See next page.) 



On Progressive Speed Trials. 



128 



/ 




The reason why the carve of the logarithms of the pressures hoh 
so straight^ is that it contains a very elongated I'egion of contrary 



124 On Progressm Speed TViob. 

flexure, and at a contrary flexare the cunratore is always zero ; and 
it will be seen that whereas if the ship's resistanoe, and the steam 
pressure due to it» remained proportional to the (speed") up to the 
highest speeds, the curve of logarithms of pressures would turn down- 
wards, as sketched ; yet inasmuch as the resistance soon begins to 
increase faster than (speed*), this circumstance provides a growth of 
pressure ordinates at the higher speeds, such that^ in the cuire 
given by the logarithms of the pressures, the downward tendency of 
the curve is more or less obliterated, or (according to circumstances) 
even reversed 

It is interesting to trace the history of this curve in its mathe- 
matical details, and this may be simply done, if we assume, as I feel 
sure we ought to assume, for the lower speeds at least, that 
P (or P + rp by your notation) = o + te*. 

This being so, your curve of pr^ure-logarithms is defined by the 
equation, 

y = log (a + hv^) ; 

and observe, for convenience of writing, I shall adhere to the use of 
hyperbolic logarithms in the discussion. This being so, 

dy 2hv 

dv = ir^w (^> 

by (2) we see that the curve has a contrary flexure at the point 
where (a — W) = 0, or r, say v\ = J-y and where the corresponding 

value of y, say y, = log 2 a ; also, ■£, = ^ a- J- 

a 
If we take the equation of the tangent to the curve at the point 
where this contrary flexure exists — that is, the point where the 
co-ordinates are y and t/ — the equation is, 

where h is the height at which the tangent cuts the axis of Y. 



On Progresiwe Spesd Triak. 



125 




In ibis equation we can determine h by inverting the conditions 
which belong to the point y^ v\ and where, since it is also a point 
in the corye of pressure-logarithms at the point of contact, 

y = log (a + bv') = log 2 a. 
Substituting this value in the equation of the tangent, 

l6g(2a)-h = J^-Jl=l; 

or, A as log (2 a) — 1. 
Now, in your way of estimating the constant friction (which in 
your notation is f), you make h &= log f, but in reality f = a in the 
equation of the original parabolic curve, and A + A' = log f (see 
sketch). 

Y . 




You will perhaps say that you have as goo4 a right to your 
method as I have to mine ; and the only reply I have is that the 



126 On Progresrive Speed Thais. 

assamption you make — ^namely, that the line of pressure logarithms 
is a straight line, and continues straight till it cuts the axis of Y at 
the height &-^is a gratuitous assumption, founded on no mechanical 
or dynamical principle ; but that my conclusion rests on the justi- 
fiable and indeed plainly correct assumption that (at all events for 
low speeds) P = a + fto*. If this assumption be a true one, my 
conclusion is plainly true also ; and it is only because I think you 
will, on reflection, probably agree with me as to the constitution of 
P, that I have a right to intrude this long discussion on you. 

Without further apology, therefore, I will continue to work out 
in detail the differences which arise out of the two modes of treating 
the question, as they issue in reference to the case of the ^'Merkara^" 
which is one we have both investigated ; and in treating it I will 
take the steam pressures in the terms in which you have expressed 
them, as '' unit piston pressures, P + rp," but for simplicity I sym- 
bolise the figure as P. 

According to my way of treating them, then, it is only necessary 
to see what are the elements of the parabola which is expressed by 
the equation P s a + ^v"; that is to say, to determine (a) the pres- 
sure due to constant friction, and (b) the factor which expresses the 
relation of the residue of the pressure to the square of the speed. 

As in point of fact the resistance of the ^' Merkara " does not, up 
to 9 knots, sensibly deviate from the quadratic law (as I know by 
experiments with her model), these values may be as exactly deter- 
mined by what I called the algebraical method (see page 57), as by 
the geometrical, and I adopt the former. 

The two experiments, at 6-2 knots and at 9*2 knots, give data 
which when substituted in the equation V = a -{• bt^, result in the 
two equations following. 

The data are, 

(1) Speed, 6-2, Pressure, 22-79, 

(2) Speed, 92, Pressure, 38-12, 
and the equations are, 

(1) 22-79 = a4-6x (6-2)*. 

(2) 38-1.2 = a -H 6 X (9-2)3. 



On Progressive Speed Trials, 127 

The solution of the equations gives 

a = 10-04 b = ^ 



30136 
= 0-3318, 
and the equation of the parabola is 

y = 10-04 + 0-3318 v*. 

Here, 10*04 is the constant friction pressure. 

If I frame your curve of the logs of the pressures, these values of 

a and b supply the data. 

By the equation in p. 61, . 

A = log 2 a + 1. 

Beminding you again that I am using hyperbolic logarithms, 

h= 1-9997, 

and since h = log qP, ^P = 7*39 ; and 7*39 is the pressure due (by 

your method) to the constant friction, whereas by mine it is 10-04. 

The equation of the straight line which is tangent at the contrary 

flexure, and which cuts the axis Y at the height h — ^the straight line, 

in fact, which fits the logarithms of the pressures of the " Merkara " 
trials — is 

,_,.«, = . yiT^ 

= -1818 z;; 
and if the ordinates of this line be calculated out for each of the 
values of v, 0, 1, 2, &c., and if again we set side by side with these 
values the tabulated values of log. P, calculated for the same values 
of V, by the equation P = a + ^ we get the following columns, and 
you will see how closely the two run together for all the lower part 
of the curve for which the ^' Merkara " trials gave data, and how 
resolutely they differ for all the still lower values of v, namely values 
below 6*2 knots. 



128 



On Progresrite Speed Trials. 





Ordinates of tan- 






gent on Mr 






MansePs straight 


Ordinates of curve 


V. 


line, which appro- 
ximately fits the 


formed hy log P 
when P-a-f-Ot;». 






logaof "Merkara" 






Preasnre. 







2-0000 


2-3065 


1 


2-1818 


2-3389 


2 


2-3636 


2-4809 


3 


2 5454 


2-5672 


4 


27272 


2-7311 


5 


2-9090 


2-9085 ! 


6 


3-0908 


3-0901 


8 


3-4544 


3-4426 


10 


3-8180 


3*7663 



It will be seen ihat the figures agree very closely for a long range, 
and if the second coltunn were shorn of the figares for o == 0, 1, 2, at 
the beginning of the scale, and = 10 at the end, the intermediate 
figures when laid off as ordinates at their appropriate speeds would 
be suggestive of an absolutely straight line^ and yet they would 
lead into error any one who adopted and relied on the suggestion. 

There are two other columns of tabulated figures which I will 
tabulate accordingly. 

(1) The series of pressures calculated by the equation P = a + ^ 
the other, the numbers^ of which the ordinates of the straight line 
are the logarithms, and which are implicitly assumed to have been 
the pressures, if you assume the line given by the logarithms to have 
been straight throughout. 

You will observe that the figures in the two columns agree very 
closely at the medium speeds, that at the sero end of the speed 
scale there is a difference of about 1 in 8*3, and at the 10 knot speed 
there is a difference of about 1 in 20. And it is deserving of notice 
that if we take the differences between the corresponding pairs of 
figures in the table in p. 23, while the difference at the zero end of 
the scale is there only about 1 in 7, the difference at the 10 knot 
speed is only 1 in 75, so that by converting the pressures into their 



On Pragresme Speed Triak. 



129 



logarithms an operation has been performed which masks or reduces 
in visible magnitude the differences of the pressures, especially of 
the larger pressures, and makes it easy to overlook, especially in a 
graphic exposition of results, linear or geometrical quantities which 
represent quantities which are really large but which aa^ made small 
by their logarithmic dress. (I have already referred to this circum- 
stance in pages 11 and 12.) The table is as follows : — 



r. 


Presoares inferred 

from the 

Ordinates of the 

8trai«;ht line, 

regarded as the 

logs of the 

Pressure. 


Pressures calcu- 
lated by tbe 
etjuatioii 
P=a + 6t7«. 





7-39 


1004 


1 


8-86 


10-37 


2 


10-63 


11-37 


3 


12-75 


13-03 


4 


15-29 


16-35 


5 


18-33 


18-33 


6 


21-99 


21-98 


8 


31-63 


31-27 


10 


45-50 


4322 



Observe, this illustration of the consequence of converting pres- 
sures into their logarithms, which I just now pointed out, is a real 
one, even if it were shown that my equation P = a + ^, which I 
used in calculating the tables is erroneous — for the point of the 
illustration is that it shows how a given difference in the large pres- 
sures is reduced in visible magnitude by that method of representing 
the pressures. 

To complete the comparison, I have pretty carefully *' plotted " the 
two pairs of " tables " on the accompanying sheet of ruled paper — 
which, however, as I have not made a duplicate, I will ask you to 
return to mc when you have sufficiently examined it. 

I see there is one point in reference to the curve of pressures 

which I have omitted to notice. 

18 



130 On PrOfji'cssive Speed Trials. 

You will see that the curve calculated by the equation P = a+^ 
cuts exactly the two points of pressure given by the •* Merkara " 
experiments, for the 6*2 knots and the 9-2 knots ; this of coarse it 
was bound to do, because it was calculated from them ; it, however, 
cuts below the point which belongs to the 11*09 speed, and still 
more below that which belongs to the 1291 speed. On the other 
hand, the curve built on the pressures calculated back from the 
ordinates of the straight line, regarded as pressure logarithms, cuts 
distinctly above the experimental pressure for the 9*2 speed, and if 
continued would cut a little above that for the 11*09 speed, bat 
would cut a little below that for the 12*91 speed. 

The meaning of all this is that as a matter of fact, the resistance 
of the ''Merkara" is practically as the square of the speed, up to 
just 9 knots; above this speed, the resistance increases in a higher 
ratio, and thus of course for higher speeds deviates from the parabola 
which correctly expresses it so far. On the other hand the line 
which is defined by the logarithms of the pressures is not absolutely 
straight though it is nearly so, and when an absolutely straight line 
is substituted for it, and the pressures are calculated backwards from 
the ordinates of the straight line, the resulting pressures are far 
more different from the true pressures than the logarithmic line is 
from the assumed straight line, and the definite tangible error is 
thus introduced into the data. 

Nevertheless it happens that the series of pressures which are Uius 
obtained from the straight line indicate a resistance which grows 
more rapidly than as the square, and which thus has a rough sort of 
agreement with the real growth; only the agreement is arbitrary 
and haphazard, and has no real relation with the special law of 
pressure which each form of ship requires (a law which is materially 
different for different forms), and will certainly contradict the law 
for almost any possible form of ship as the speed increases. 

To give greater clearness to the view I am endeavouring to 
express, I send with this a couple of lithograph sheets (extracted 
from a report of mine to the Admiralty, sent in a year ago after I 
bad made experiments with a model of the ^' Merkara "), one of 



On Piogt-essive Speed Triah. 181 

which gives Uie lines of the '' Merkara," and of throe other types of 
form which had been included in our general course of experiments 
here — the other gives the resistances of ships of all four types, the 
^ Merkara/' and the other three, all reduced to ships of the same 
displacement, namely 3,980 tons. 

In that report I went fully into the question of ''constant friction/' 
treating it on the principles which I have endeavoured to explain in 
this letter, so I need not send you the report, since the greater part 
of it has been ahready said here, and this in conjunction with the 
discussion of new matter which has grown out of your different 
treatment of the same data. 

I have, however, added to the resistance diagram four lines based 
on the logarithms of the four resistance curves according to your 
method. 

These lines are all so nearly straight in appearance for the greater 
part of their length as to offer great temptation to treat them as 
straight lines in the manner which your paper describes, and yet it 
is plain that in doing so the exactness and the significance of the 
original curves of resistance would be lost and &lsified. 

In calling attention to this diagram, I ought perhaps to refer to a 
feature in the '< Merkara's " curve of resistance which will, perhaps, 
at first sight appear to you unnatural, and may lead you to mistrust 
the representation. I mean the peculiar ''hump" in the curve, 
between the speeds of 14^ and 16| knots. 

Let me say first that our experiments are made with models of 
large size — ^that of the ^'Merkara" was about 14 feet long — ^and with 
the most exact automatic apparatus for recording speed and resist- 
ance, and our work already comprises the complete investigation of 
the resistance properties of several hundred varieties of form. And 
I may say it is rather the exception than the rule to find a perfectly 
"FAm" curve of resistance. These humps occur with more or less 
pronouncedness in the case of all forms which have the sides straight 
for any length. If you scrutinise curve D closely you will see a 
trace of such a hump in the part of the curve between 11 and 13 
knots. 



132 On Progressive Speed Tridb, 

And we have been able to identify the circumstance which seems 
the proximate cause of the hump feature, which is as follows: — 

When the speed is such as to produce waves of sensible magnitude, 
that wave which is created by the bow reappears as a secondary 
wave with its crest against the ship's side — ^the position of the 
secondary crest being determined by the ship's speed, which requires 
that the wave which keeps pace with her shall have a definite length 
from crest to crest 

When the secondary crest abuts against the parallel part of the 
ship's side, (if she has parallel sides, like the ^' Merkara's/') the 
pressure due to the wave height has no local eflfect on the ship's 
resistance — it neither pushes her backward nor helps her forward — 
but when her speed is so increased that the wave length is so far 
increased that the wave crest infringes on or abuts against the 
converging lines of the run, then the extra head given by the wave 
crest becomes an auxiliary propulsive force, and makes a sensible 
diminution in the resistance. 

Now I have said all I have to say in reference to the question of 
the ship's natural resistance and to the mode of treating the steam 
pressures supplied by experiment. 

There remains a point of great importance, of which you make 
no mention in your paper, and to which perhaps your attention has 
never been directed. 

I refer to the augmentation of resistance which results from the 

action of a screw or other stern propeller, from the circumstance that 

the stemward pressure which it throws on the water on which it 

operates, necessarily lessens the natural pressure of the contiguous 

water against the ship's stem post, and against the nearer parts of 

her run. 
It has so long seemed to me inevitable that 'the loss of pressure 

must be thus produced, and it has been so long known to me that it 

does in fact exist to a most formidable extent, and yet I have found 

it so difficult to get shipbuilders to attach to the circumstance the 

importance it deserves, that I am almost weary of arguing about it. 

And now, as this letter has already run to a portentous length, I 



On Progressive Speed Tiials, 188 

will, instead of arguing about it^ merely give you the categorical and 
quantitative proof of its existence which our experiments have 
supplied. 

To make this clear, I must roughly describe our dynamometric 
arrangements. 

Our " sea " is a covered tank or canal, nearly 300 feet long \ — the 
working length is about a mile on the scale of ike model's dimensions 
compared wiih the biggest Mps ;^it is 36 feet wide and 10 feet deep 
— as detp in proportion to the model as the Bntish dhannel to the biggest 
ships. 

A railway, suspended from the stiff roof, traverses the length of 
the tank 15 inches above the water. 

A truck runs on the railway, driven by a double cylinder engine 
by a wire rope on a drum, which by help of a delicate governor and 
change wheels, administers any required steady speed to the truck. 

The model is carried forward by and under the truck, being guided 
or kept from sheering by a light counterbalanced frictionless knee 
joint motion at each end (which allows perfectly free motion in the 
vertical plane, or fore and aft, but is inexorable against sheering), 
and being pulled forward by a dynamometer spring, the extension 
of which by the model's resistance is automatically recorded. This 
spring is virtually the tow rope^ and indicates the towing strain 
simply. 

Let us now suppose that we have thoroughly determined the natu- 
ral resistance of say the '^ Merkara " model at all speeds. 

We now bring forward and " couple on " a second truck, under 
which there is bracketed down into the water a horizontal shaft, 
which I will call a screw shaft, which protrudes forward ahead of 
the truck, and is at the level which would be that of the screw shaft 
of the model if she had one. A screw, suitable to the model, is 
fitted on the end of the shaft, and the screw truck is coupled up 
astern of the dynamometric truck with the model under it, at such 
a regulated distance that the screw occupies exactly the position 
behind the model which it would occupy if the model were regularly 
fitted with a screw. The screw, however, does not touch the model. 



134 On Progresifive Spud Trials. 

Aa the two trucks ran on together, the screw is made to revolve 
by independent power, at any required speed, being driven hj gear- 
ing connected with the truck wheels, and it may be kept going at 
the speed proper for propulsion, or at any greater or less speed. 

The frame which carries the screw shaft is delicately suspended, 
so that it possesses a power of moving horizontally under its 
truck, in a fore and aft direction, and the position of the frame 
is defined by a djmamometric apparatus which automatically records 
the drag or thrust of the screw. This rough sketch may help you 
to follow the description. 



l>yAIAMOMiT£ft 



TAOC/C 







SCft£W SMArr 



SfYli Gt*> 



This apparatus, in the first place, brings out in the clearest way 
the augmentation of the model's resistance to which I have referred. 
When the screw is so speeded as to produce a drag equal to the 
model's total resistance ; that is to say, to the natural resistance + 
the augmentation, it proves that from 40 to 50 per cent, has been 
added to the resistance. The augment is, in fact, 40 or 50 per cent, 
of the natural resistance at each speed. 

In the next place the apparatus brings out in the clearest way the 
value of the wave or current which follows the ship, on which I am 
glad to see you lay stress. 

I frequently show the following illustration which simultaneously 
exhibits both the augmentation of resistance, and the increase of 
screw drag which results from the following current at given speed 
of screw. 

We first run the screw truck with its screw, but without the 
model — ^and we speed the screw to its true pitch — so that it neither 
drags at its frame nor pushes it back, but simply cuk the water. 



On Pt'ogressive Speed Tricils. 135 

We then harness on the model; and repeat the run. 

The moders naiural resistance at the speed (indeed at all speeds) 
is already known. Now that it has the screw at work behind it, 
the mutual reaction of the model and the screw becomes apparent. 
The screw, instead of merely cutting the water, is exerting a strong 
drag, probably more than half of what is required to overcome the 
model's natural resistance, the whole of this drag being due to the 
screw's encounter with the current which the model has created, for 
if the current were not there the screw would have no drag. The 
resistance of the model has received an augment of some 20 per cent., 
though the conditions of resistance are unchanged except by the 
drag which the screw exerts on the water behind it. 

We shall shortly pursue this question with more completeness and 
exactness than we have already attained. There have been some 
difficulties in ascertaining the exact drag of the screw, because we 
have to clear it of the resistance of the thin knife-like brackets 
which carry it, and of the spindle and bevel gear which drive it, and 
to obtain this clearance with exactness, that is to say, to obtain its 
exad measure, has involved 'some difficulties which we have only 
recently seen how to master ; but the broad features of the experi- 
ment are glaringly conclusive, and the residuary errors or uncer- 
tainties are relatively inconsiderable. 

I may add that if the screw is removed stemwards to a space of 
about one-fourth of the model's beam, the augmentation of resist- 
ance is greatly diminished, and yet the benefit realised from the 
following current is scarcely if at all impaired. 

When I began this letter I had not fully calculated the length to 
which it would run, and perhaps if I had done so I should have 
hardly felt entitled to seek to impose on you the burden of reading it. 
But it seems to me of such high importance that the subject of ship 
propulsion and ship resistance should be treated in a really scientific 
manner, and that therefore those who are endeavouring to arrive at 
and disseminata the true principles of the treatment should exchange 
ideas on the subject and come as far as possible to an agreement 
respecting it> that one should not be nervously hesitant about making 



136 On Progressive Speed Trials. 

8ach communications. Only, I must add, I hope yon will not feel 
obliged to write at as great length in reply, for probably that would 
be too heavy a tax on your time, already perhaps too fully occupied 
by the demands of business. 

I am yours truly, 

W. FilOUDE. 



The discussion on this paper was resumed on 27th January, 1885. 

Mr Mansel said— The printed documents of last month's pro 
ceedings of the Institution furnished a full basis and introduction to 
the subject of discussion for to night, and showed quite clearly that 
while there existed a subject of scientific interest in dispute between 
the late Dr Froude and myself, Mr William Denny had enlarged it by 
a second question, of little general interest, which was personal 
between Mr Denny and myself. This latter most people, I think, 
would allow had better have been avoided ss much as possible ; and, 
better still, ought never to have been raised, for, I submit, any one 
who reads Dr Froude's letter will see, that while asserting the inde- 
pendence and superiority of his own interpretation, Dr Froude 
advances nothing which can be construed into a support of Mr 
William Denny's assertion, that my investigations on the same 
subject were founded upon notions of Dr Froude's method, which 
Mr William Denny had communicated to me in the autumn of 
1875. When Mr Denny made this charge of plagiarism against 
me, his attempted explanation on my methods at once led Dr 
Froude's truer instinct in such matters to the real point at issue 
between himself and me, and he put the question as to the law 
of the resistance which I had assumed, stating quite truly ^^ it 
must involve some such rule." Mr Denny admitted ^* he did not 



On Progressive Speed Trials. 1 37 

know the principle," also, "in every case, with one exception," 
the data had satisfied a remarkable condition, which he had stated 
to be a consequence of my principle. If so, Mr Denny ought to 
have been more guarded in his statements, and sought further 
information before, in my absence, making me the subject of an 
infamous charge, the existence of which, in a definite shape, only 
came to my knowledge about nine years afterwards ! Mr Denny 
has printed a letter of mine, dated 17th May, 1875, in which I gave 
him an extended application of the formulas I advanced in the dis* 
cussion of his paper on the " Difficulties of Speed Calculation,'' in 
this institution in April, 1875. Mr Denny's answer to that letter 
was accompanied by the trial data of two Chinese vessels, the 
"Pau Tah" and "Fung Shun," the latter of which was tried on 
25th September, 1875. I replied shortly after, but having only a 
pencil draft of my letter, cannot specify the exact date.* Cer- 
tainly, however, it was before my interview with him on his return 
from England, when he spoke of Dr Froude's graphical solution 
of my published equation, which, by Mr Denny's own admis- 
sion, I at once challenged as unsuited for its object. To have 
written this letter after this meeting would, on my part, have 
exhibited a height of folly or depth of humility which I shall never 
try to attainj Mr Denny's answer to my letter of 17th May, 1875, 
was somewhat critical thereon, for which he made apology, and 
hence the tone of my reply ; which, omitting some irrelevant 
matter at the commencement, read thus : — 

'' Your data of the Chinese vessels and last note and enclosures 
came to hand in due course, and I will forward you something on 
same shortly. Meanwhile I send you a few notes, which will pro- 
bably be of interest. Don't imagine that I am in the least offended 
by any criticism that can be offered, so long as it is honest and dis- 
criminate ! I have found so few in our profession who will give 
themselves the trouble to think at all, on scientific matters, either 
correctly or otherwise, that I have real pleasure in their discussion, 

♦ Mr Wm. Denny having, since the meeting, forwarded the letter referre 
to, it was sent to Mr Mansel for his insi)ection» The date is Dec. 4, 1875.— Ed. 
ID 



138 On Progressive Speed Trials. 

and I am only sorry that we are so much out of one another s way ; 
it is such a bore writing long explanations. 

**' Most people when they get a dose of Mansel's " peculiar " either 
turn on me with the sniff ineffable, cut bono^ which is irritating, or 
speedily exhibit symptoms of intense stupefaction, qidte bouine, which 
is pitiable; but blessed are they who expect little. There is a system 
of curve analysis, which is very applicable to the cases we are discas- 
sing, namely, taking the abscissas in natural numbers, and measuring 
the ordinates by a logarithmic scale : the curves are much more easily 
drawn, and their relations exhibited. I send you speed curves of the 
<Goa,' 'Hawea,' 'Merkara,' and 'Mecca,' drawn in this way; these are 
denoted by the blue curves, actual observation spots being noted by 
the small circles. The red curves next to these are the calculated 
values of £,* or power expended on the vessel. The black curves 
are what I hold to be the value of the work done on fluid resist- 
ances, distinguished in my notes as Ef and Em, but Wf and W^, 
!>., work on friction, plus work on movement^ is a more correct 
notation, as power should be equated to work. Between the black 
carve and the red we have the values of the quantity E^,, which 
I call the recovered power. You notice correctly that I have made 
an alteration on its value. When I first examined your ' Goa ' I 
thought proper to give the after term the value 



{-^-'4i:^A.}(.««|y. 



This gives very close results with some of your vessels, but it does 
not answer over a great range of vessels so well as the simpler 
formula : — 

I 200 «* V + (100 — a) A« } (-2059 ^V. 

In later calculations, I find it simpler to take out the last constant- 
and put it under the form, 



ra*y (100-a) WE,y 
1700 "^ 140,000 ^ )\^)' 



I enclose you the ' Mecca's ' calculation as an example. 
^' Your remarks as to application of the expression of the term 



On Progressive Speed Trials. 189 

Ey are acute and quite proper, from your point of view. It is 
involved and indefinite, bat I have a notion of a flank movement 
which will make these difficulties untenable ! I will close for the 
present by marking on the several vessels the straight line which 
gives the relation between V, N, B, and its equation on the severa 
vessels* Yon cannot fail to observe the beautiful certainty with 

E 

which the spots or experimental values of logs ^ fall in the straight 

lines. On the ' Hawea,' up to about 10^ knots, we have the same ; 
after this, notice the divergence of the ends by E from its fair line, 
and the corresponding rise of the red spot above its line; also, the 
rapid diminution of the recovered power line about this spot. This 
is the mode by which I would exhibit the effect when a vessel is 
driven beyond a speed corresponding to her dimensions and fine- 
ness. Your * Chinee ' gives another excellent illustration, of which I 
cannot give you the result now. The correlation of a lot of facts 
will be necessary to further remarks*" 

As will be seen, this letter contains an outline of the mode of 
investigation fully followed out in my paper in spring of 1876 ; and, 
in so far, is an answer to Mr Denny's inquiry for information as to 
my working out of this matter, prior to the interview when we dif- 
fered over Dr Fronde's method. I shall now follow with a short 
essay on an extensive subject : — 

NEW DEPARTURES IN NAVAL SCIENCE. 

I prelude this subject with a little myth, and its moral On 
hearing the Templar's latest intelligence from seat of war in the East 
— truce for fifty years concluded with the Paynim— " Jester Wamba^ 
naively remarked : Inasmuch as in his lifetime he remembered three 
such treaties, he must needs be getting a very old man ! And so it 
is with workers in the obscure fields of naval science : they become 
cognisant of so many vaunted new departures, if only a small 
portion of those represented wise directed labour over some manifest 
mystery, Jacob like wrestled with and not let go till the dawn came 
with a vouchsafed blessing : the world had certainly been older, and 



1 10 On Progressive Speed Triais. 

mankind probably wiser. But, in recent times, new departures do 
not seem to mean much : fresh minds recognising old facts or 
fancies, thinking much of them and more of some real or supposed 
novel point of view in which they are managed to be presented ; 
and. in the end, apparent progress turns out to have been mere 
marking time or scientific goose step, not by any means steps in 
advance ; and, in cases, doubtful whether they have not been retro- 
grade rather. 

On the first applications of steam to ship propulsion, the successive 
tentative experiments with paddle vessels of increased dimensions, 
power and speed, were correlated and compared by the reasonable 
hypothesis that, for different vessels at different speeds, the power 
would be foand to vary in the ratio of the products of the square of 
a lineal dimension by the cube of the frpeed : and, in the case of 
similar shaped vessels proportionately immersed, and having engines 
and propellers of like efficiency, the co-efficients of such formalas, 
(usually known as the Admiralty formulas) ought to be constant. 
Also, since the square of a lineal dimension was involved in the 
immerged mid-ship area, the immerged surface of hull, or the two- 
third power of the displacement, it was a matter of indifference 
which of these elements, or even a combination of them, was 
employed, as the hull factor in this comparison. Experience, how- 
ever, soon exhibited many marked deviations from this assumed 
law, which could not reasonably be accounted for by slight structural 
variations which might exist, and it came to be well understood that 
the fundamental hypothesis, in some way, was faulty, and that great 
care was necessary in order to draw correct conclusions from its 
indications. 

In a " First Report of a Committee of the British Association," 
published in 1869, ''separately for the use of the Institute of Naval 
Architects,'' an extract from a pamphlet by M. Dupuy de L6me is 
given, stating <^ It is near the truth to say, that, for similar forms, 
the resistance per square m6tre of midship section, at the same 
speed, decreases as the vessel increases, in the ratio of the square 



On Proffremve Speed Trials. 141 

roots of the radii of curvatare of its lines, these radii being them- 
selves proportional to the lineal demensions of the ships ; it is there- 
fore wrong to compare the resistance of different ships by many of 
experiments made on models to reduced scales/' and the same 
author refers to long anterior lectures, in which this subject was 
discussed by M. K^ech. In this report at page 28, it is also stated, 
'' and some time later (than 1827-28) M. R^h pointed out that 
models of different sizes intended for comparison should be made to 
move at velocities varying as the square root of their lineal 
dimension : in this case the actual resistances would vary as the 
cube of the lineal dimension. This would follow from the theory of 
the resistance of submerged bodies on the supposition that the 
resistance varies as the square of the speed." 

Let us suppose two similar vessels of different sizes, the power, 
lineal dimension, and speed of the larger and of the smaller being 
denoted by the letters E, L, V, and e, 1, v, respectively. 

Stated as analogies, the original hypothesis being : — 

(1) E:e::L9V»:Pv3. 

By Rfeech's hypothesis, concurrently, we ought to have 

(2) V:v::VL : VL 

Which, being fulfilled, (1) then changes into 

(3) E:e::Li :\K 
Since, by (2), V» : v^ : : L* : 1*, 

consequently, the y^ede of similar vessels being in tlie ratio of the square 
root of a lineal dimension^ the powers for those speeds will be in the ratio of 
the seventh power of their square roots. 

For example—Suppose three similar paddle vessels, 200, 250, and 
300 feet long, respectively ; also, that the one 250 feet long is driven 
10 knots, when the engine developed power at the rate of 1000 
indicated horses. 

Distinguish the elements of the different vessels by the suffixes 1, 
2, and 3, then the speeds being in the ratios defined by (2), 
Vi : V, : V3 : : ^/200 : >/250 : 's/SW, 

which the factor . - changes into 



1 42 On Proffrrsswe Speed Trials. 

::10/!^:10:10 /^ 
V 2;:0 V 250 

: : 8*945 : 10 : 10*955 knots. 

The respective comparative speed for the three vessels. By (3) the 

corresponding powers for these speeds, 

El : Ej, : E, : : (200)* : (250)* : (300)*, 

1000 , 
which the factor- > changes into 

: : 458-3 : 1000 : 1893 indictd, horses. 

But the simplest applications of these principles to practice is 
enunciated thus : Similar vessels driven at speeds proportional to the 
square root of a lineal dimension, will have their Admiralty co efficients 
alio/ the same value. 

This is easily seen to be the case : suppose the 250 feet vessel had 

an immerged mid area of 450 square feet, the midship.area formulas, 

«, . , mid area x speed^ , . , 

coefficient = obviously are : 

power •' 

/200\* /300\« 

co-effict. = ^^n250)-^^^ ^ = 4j0>a0-= 450 (^,)x 10-955 ^^^^ 

458-3 ^^^ 1893 

Now, instead of being driven at the respective speeds found above, 
more power is developed in the 200 feet vessel, and less in the 300 
feet one, so that the speeds of all three are 10 knots : then, the one 
is overdriven and the other underdriven by about one knot from the 
speed which would justify the one value of co-efficient ; and^ if from 
the experiment on the 250 feet vessel, we had set out to calculate, 
by formula, the power for the other vessels ; according to the experi- 
ence of naval architects a less co-efficient would be adopted for the 
less vessel and a larger co-efficient for the greater : tantamount to 
saying ; in the same vessel, the Admiralty coefficients diminidi with the 

increased speed. Or, we may write this, co-efficient jp: — 

where f{v) denotes some unknown function of the speed, and the 
formula would stand thus : 



On Progressive Speed Trials, 143 

mid area x speed "^ mid area , ^ ^ ^ 

Nowy(v) increases with the speed ; and, hence, the power irureases 
in a fasten* ratio than the cube of the speed. 

This is the necessary deduction from Bach's hypothesis ; but, to 
a limited extent^ agrees with the facts of experience, and the special 
explanations generally advanced, are admitted failures. The report 
already referred, to, commences by stating *^ resistance may be treated 
in two ways . . . either in gross, as regarding the power 
required to drive a vessel of certain force and dimensions at a 
specified rate ; or, in detail, as regarding the exact way in which the 
vessel and propeller act and react upon the water which they disturb 

... the former of these is not understood with any reasonable 
degree of certainty, and the latter also being far from being settled 
with precision." Beech's hypothesis is strictly the one which under 
the name of '* Fronde's Law " has been much lauded in recent years. 
For example, in the " Watts Anniversary Lecture " at Greenock, by 
Mr Wm. Denny, it is stated : *' model experiments had been made 
before Mr Froude took this matter of resistance of vessels in hand, 
but it was not till his time that we were enabled to relate accurately 
the resistance of a model to that of a large size, or to that of a full- 
sissed vessel. Partly by speculation and partly by experiment Mr 
Froude discovered the law of this relationship. What Mr Froude 
discovered amounts to this, that for vessels of the same proportional 
dimensions, or, as we say of the same lines, there are speeds appro- 
priate to these vessels which vary as the square roots of the ratio of 
their dimensions; and at these appropriate speeds the resistances will 
vary as the cubes of their dimensions." This is exactly what R^ech 
deduced some 50 years before. It seems to me, those statements are 
not fair towards the memory of M. Btech and very injudicious to- 
wards that of Dt Froude. In all this inquiry the primary object is 
to enable us to foretell the power required to propel a given vessel 
at required speeds, and to compare the efficiency of different vessels. 
Dr Froude's method of solving the first of these objects by means of 
model experiments, only yields approximations by the use of 



.144 On Progressive Speed Trials^ 

empirical assumptions, which are questionable both in point of 
novelty and accuracy. As shown, put in the most direct shape, the 
principles amount to these : when the speeds of similar steam vessels 
are in the ratio'of the square root of a lineal dimension, the power 
for these speed8,"are as the seventh power of this square root; and, 

the " Admiralty co efficients," such as, co-efficient = pe^_ 

power 

have the same value.* Now, employed between vessels of not 
greatly varied dimensions and forms when subject to like actions 
and reactions and losses in machinery and propeller ; there may be 
a reasonable expectation of agreement between deductions obtained 
by these principles and experience, which can not be expected from 
their partial application to a small scale model, in which the absence 
of the propeller entirely alters the character of the phenomena, and 
leaves the determination of the power for the corresponding vessel 
much a matter of guess work. Dr Froude's signature is attached to 
this report in which M. Reech is credited with the discovery and 
publication of this so called '' law,'' and though Dr Froude dissented 
from the conclusion of other members of committee ; that for certain 
data full-sized ship experiments were desirable, and in a supple- 
mentary report upheld the value of model experiments, which he 
declared <*when rationally dealt with, by no means deserve the 

* To illustrate this subject let us refer to a recent illustration from a paper 
by one of Messrs Denny's employees. A 12-feet model is drawn through the 
water at three knots with an observed strain of four lbs., hence 4 x 3 x 101-3 
foot pounds per minute; that is to say, an indicated power of *036S3 indicated 
horses, and since \/T2 : Vsoo : : 3 : 15, a 300 feet similar hull^ would be 

(800\ X 
12 / ^*®"^ "^ -03683(5) ' 

= 2879 horses. Also, if a be the immerged mid area of the model, 

(303 \* 
„„^,, .„,^ ¥) 15' = 733 a for both. 

power V6Wi6 ^^g 

To 2879 horses as above, is to be added slip losses, action of propeller and 
working engines increasing the gross, so as to compare with experience, by 
some very doubtful assumptions; amounting on the gross to something very 
like an old rule " guessing the half ami doublvtg it" 



On Progresmc Spud Trials. 145 

misirost with which they are usually regarded " so far as the model 
is implicated in his explanations, the dealing is simply the direct 
application of B^h's hypothesis. Beyond this, however, there are 
other deductions, which, whatever merit they possess, may with 
more propriety be ascribed to Dr Froude. I would here remark ; 
beyond giving a good summary of the views of some eminent men 
who have interested themselves in naval science, the labours of this 
committee do not seem to have gone far to advance that science. 
Indeed, properly examined, we have statements contradictory to a 
degree ; and, viewed as a whole, singularly adapted to unsettle in 
men's minds, any small degree of certainty which might there exist 
on any particular branch of the subject considered! Take, for 
example, the very innocent looking deduction ** vessels of a certain 
form" (corresponding to the minimum of resistance) have a ''fair 
entrance and run and an absolute length of not less than the length 
of the trochoidal wave moving with the same velocity." On employ- 
ing one of these torpedo boats, which are uncommonly efficient with 
one-third of the length of the trochoidal wave moving with its 
velocity^ to blow the superimposed length condition into nebulosity, 
we are then confronted with Dr Froude's conclusions '' an abnormal 
form (suggested simply by the appearance of water birds when 
swimming) if moving with a high, but not excessive velocity experi- 
enced considerably less resistance than the wave line form, the 
accredited representation of the form of least resistance particularly 
at high speeds.** Also : '^ for symmetrically shaped bodies of < fair * 
lines, not excluding by that description certain very blunt ended* 
ovals, when wholly submei^ed, the entire resistance depends on the 
conditions of imperfect fluidity, of which surface friction is the only 
one so considerable that we need take account of it, if we deal with 
bodies of rational dimensions." Looking at the form figured by Dr 
Froude would suggest to some minds exceedingly strong doubts as 
to the value of model experiments ; and the statements quoted are 
samples of a soil suited to the development of *' new departures ** 
which anon shall blossom and fructify into ** Popoff kas," length and 

breadth synonymous ; and war ships ^' short and handy *' which a 

20 



146 On Progresmve Speed Trials. 

Beed, not shaken by, bat controlling the winds, shall extd mag- 
niloquendy; and Old Neptnne, most misanthropical of ''pike 
keepers," by his onpublished table of rates, shall Ml moat exorbit- 
antly. Nay, worse than that, cap his misdeeds by Lady ** livadia," 
peerless amongst the tribe, being treated with frightfiil contomely. 

We hear of the glorious ancertainty of the law, bat whenever 
want of certainty is at a jvemiam, or reqaires to be iUostnted, the 
laws affecting the elements of steamship propulsion can be confi- 
dently referred to as having attained a stage which, cpntrasted with 
glorious, may well be termed seraphic This does not apply to 
deeper considerations involved in the question, but to simple data 
lying on the threshold of the subject, which ought to be matters of 
honesty careful observation. For example, what is the amount and 
law of the resistance due to the friction of a square foot of a clean 
painted iron surface, at different velocities? 

Eighty-seven years ago the extensive and costly eiqperiments 
associated with the name of Beaufoy were instituted, and inclu4ed 
an answer to the kindred question pertaining to timber vessels, 
which, if accurate, ought to furnish a dose approximation to our 
question. We may first consider the values deduced from his own 
experiments by Dr Froude some years ago. In the Transactions 
of the Institute of Naval Architects for 1874; there is a carefully 
drawn curve of Dr Fronde's deduced values of the fluid friction upon 
immersed surface of H.M.S. ''Greyhound." On measuring the 
ordinates at various speeds up to 12*64 knots, as carefully as the 
smallness of the scale permitted, the coppered surface being taken 
at 7260 square feet as a divisor, yields the following tabular values 
as the friction on one square foot at the respective speeds noted, as 
follows : — 



On Progressive Speed Trials. 
Table L 



147 



Speed 


400 


640 


880 


1120 


1280 


feet per minate 


or 


3-94 


6-32 


8-69 


11-05 


12-64 


nautical milea 


Frictioo 


•130 


•300 


•602 


•768 


•951 


lbs. 


Values by formnla f = -0127 V» -^ 


Friction 


•131 


•293 


•503 


•757 


•950 


lbs. 



From this we see that the above simple formula^ in which the 
speed y is taken in nautical miles, reprodaces ¥rith great accuracy 
the curve values ; and for 10 knots the calculated value is fs*6d81b. 

Taking the Beaufoy experiments in 1798 upon a painted 50 feet 
plank, at 4 and 8 knots, extended by induction to 10 and 16 knots, 
the values seem to be : — 

Table IE. 



Speeds, 


4 knots. 


8 knots. 


10 knots. 


16 knots. 


(1798) Experiments, 


•144 


•432 


•605 


1 


Formula f= -0127 vi-^ 

• 


•135 


•437 


•638 


1-415 


Formula f-V(^+3-6) 


•136 


•416 


•611 


1-411 


rormuiai- ^^^ 



In this Table II. the values of f by the 1798 experiments are con- 
trasted with the values derived from the formula f*-*0127 v^*^, in- 
volving a fractional power of the speed; and, again, with the values 



148 



On Progressive Speed Trials. 



V rvr + 3*5) 

derired from ihe fomrala f = — ^^gj — , which is Prony's form of the 

frictional equation applied to surfaces, with constants derived by me 
from the Beaufoy experiments, slightly modified by other data, and 
is noteworthy as the first formula deduced from the consideration of 
the loss of head due to the internal surface friction on long lines of 
pipes employed for water distribution. The general form was pub- 
lished by Citizen Prony, in the year I. or IL, not the Christian dis- 
pensation, however, but its antithesis — the Uberte^ egaUU, fraierviii 
affair. 

In the Greenland Dock Experiments referred to, when this ques- 
tion was experimented upon, a smooth painted plank, having about 
50 sq. ft. of surface, was employed. In 1796, when used thoroughly 
water-soaked, gave values somewhat greater than in 1798, when the 
plank was not roughened by long immersion* The highest speeds 
for which experimental values were obtained was about 8 knots; but 
extending the curve to 10 knots we have the following table :— 



Speeds, . 


4 knoU. 


8 knots. 


10 knots. 


1796, . 


•155 
•144 


•501 


•688 
•605 


1798, . 


•432 


Foregoing formula values, 


•135 


•437 •ess 



These figures justify the deduction as to the apparent law of Dr 
Fronde's curve, and show its fair agreement with these old experi> 
ments. 

It is somewhat surprising, therefore, on looking into the ^* Tran- 
sactions of the Institution of Naval Architects/' to find in Dr 
Fronde's paper *' On the Elementary Belation between Pitch Slip 
and Propulsive Effect," at page 47, vol. xix., 1878. The assumption 
that this quality, for a screw blade, '^ even when its surface is quite 
smooth, is as much as l^lbs per foot» at 10 knots, and is nearly as 



On Progressive Speed Trials. 140 

the square of the speed, and as each square foot of blade involvea 
two square feet of skin, the resistance of each is over GOlbs." Obvi- 
oufily, in the proposed case of the blade travelling at 50 knots, on 

both sides, 2 f =2 x 1^ x ( ya) =62*5 lbs., and in another place by an 

assumed co-efficient *004, this is reduced to 57*llb6. Now it seems 
to me, if the ^' Beaufoy " and '^ Greyhound " deductions are of any 
value, the true figure is very much less, viz.: — 

(50\i*7 
fo) = 197 lbs. « 

and we may ask upon what grounds the friction is doubled to begin, 
and then nigh trebled by neglecting the known and obvious fact, that 
so far as experiment goes, frictional resistance does not inci^ease so hst 
as the square of the speed ! I keep in view the fact, in 1858, Dr 
Rankine published as a deduction from Weisbach's pipe formula, 
that for a painted plate, at 10 knots speed, the resistance might be 
taken at lib; per square foot, and then assumed to vary as the square 
of the velocity. I have to submit, however, that the complete and 
exhaustive experiments on the movement of water in straight pipes, 
published about one year earlier by Mons. D'Arcy, go to show that 
the majority of the experiments upon which Wisbeach and other 
hydraulicians had based their formulas, were of such a nature that 
they must, necessarily, have given values much in excess of the 
truth. 

To illustrate this matter from another point of view. Recurring 
to Dr Froude's figure for the " Oreyhound," and measuring with as 
much accuracy as the small scale will permit, it appears that Dr 
Froude deduced that the frictional resistance upon 7260 square feet 
at the respective velocities, in feet per minute, was as stated in the 
following table ; whence, taking the product of the resistance and 
this speed, on dividing by 33,000 we have the power expended in 
overcoming this resistance, in terms of the Watt conventional horse- 
power. 



150 



On Progressive Speed I rials. 
Table of " Greyhound " Friction (Dr Proude). 



Speed in 


Speed in 


Keriatutce 


Power in 


feet per 


nratical 


in 


Indicated 


minate. 


nUea. 


lbs. 


Horaes. 


1200 


11-86 


6200 


225-5 


1040 


10-27 


4850 


152-8 


880 


8-70 


8600 


96-0 


720 


711 


2550 


55-6 



Now by this Prony form of the f notional equation, employed in 
the Clyde since 1850, and published in the Transactions of this 
Institution (March, 1876), the indicated horse-power required to 
overcome the frictional resistance on 7260 square feet at the respec- 
tive speeds noted above is given by the equation : 

indicated power = surface — A qqq — -, 

which, for the given data, employing logarithms for the calculation, 
yields the values — 



Speed in knots, 

Logsurfikce, = 
LogV«, = 
LogV+3-5, = 

Subtrftct— 
Log 68,000, = 

Log Power, = 


11-85 


10-27 


8-70 


711 


88609 
2-1472 
M861 

4-8888 


3-8609 
2H)228 
1-1359 

4-8888 


3-8609 
1-8790 
1-0864 

4-8344 


3-8609 
1-7034 
1-0257 

4-8888 


2-8604 


2-1808 


1-9875 


1-7512 



.-.Power = 224-1 151-6 

By Dr Proude = 225 5 152-8 

Differences, — 1-4 — 1-2 



97-2 


66-4 I.H 


96-0 


65-6 „ 


+ 1-2 


+ 0-8 , 



On Progressive S^eed Tiials. 151 

These differencee are animportaiit, and obvioasly less than the 
possible and probable range of errors of observation. 

I most here remark upon the extraordinary superficial views 
which Mr Denny has been pleased to express upon my methods of 
investigation^ as if they merely depended upon an after deduction, 
which, though surprisingly simple and valuable, it is manifestly 
absurd to suppose it to have no deeper meaning than a blundering 
and indefinite approximation to a straight line. Let me explain. 
It is an obvious fact, or at least can be seen with a slight exercise of 
the reasoning powers, if a vessel is being propelled by steam, the 
indicator cards of her compound engine being combined, wiQ give 
the gross indicated power being developed, in one term : 

E = 2proN(P+'p) 0) 

in which, E is this gross power, N the revolutions of the engine, P 
and p the mean diagram pressures upon a unit of the high and low 
pressure pistons respectively; d and s the diameter and stroke of 
the high pressure piston, and r the ratios of areas of the two pistons. 
Now, in the second member of this equation I have shown that in 
terms of V, the speed of the vessel and constant co-efficients, we 
have, 

(2) N = mV Log- 1 nV ; 
also, 

(3) P+rp - f Log-i (a — n) V; 

whence, it follows, by substituting these in (1), we have,. 

(4) E =bVLog-iaV; 

and also deduce the explicit value of f, which mechanicians distin- 
guish as Morin's constant, as, 

21,010 E 1 

(^' ^-" "IPr N Log-i(a-n)V- 

The perfect agreement of these formulss with the facts of experi- 
ence has been illustrated so often that it is almost a waste of time to 
adduce further examples. I will note, for a few vesssels, the values 
of a and b which enter equation (4), which is the approximate true 
form of the '' Admiralty " equation, the ordinary well known forms 



152 



On Progressive Speed Trials. 



being foundecl on a false law of tilie resistaace^ are entirely mideading 
and erroneous. 



Name of T«sse). 


Value •. 


Talneb. 


HM^. "Shah," . 


•0792 


22^63 


H.M.S. "Iris," . 


•0750 


16-30 


"Merkm," 


•0786 


16-90 


" Charles V." . 


•0842 


7-30 


" Danrobin Castle," 


•103 


7-94 


" Warsaw," 


•111 


2-97 


H.M.S, "Heroine," 


•085 


8^57 


H.M.S. "Firebrand," 


•138 


1-78 



According to this, the relation between the power and speed, say, 
for example, i^ the small vessel <' Warsaw," is, 
E=297 VLog-i-lll V; 
hence, for the following speeds, 

Trial Speeds » 4*73 7*54 9*53 10*90 knots. 



Product by -111 


= -5250 


•8869 


1^0578 


1-2099 


LogV 


= •5449 


•8774 


•9791 


1^0874 


Log 2-97 


= -4728 


•4720 


•4728 


•4728 


LogE 


=1^6727 


21871 


2^6097 


2^7201 


.-. E 


= 47-1 


1540 


8234 


525 


By Trial, 


47 


153 


324 


525 



The agreement of these figures is closer than we have any right to 
expect, considering the many sources of uncertainty which a£fect the 
data by which the relation of power and speed is determined in 
progressive speed triak. I shall now illustrate the calculation of the 
value of '^ Morin's " constant by formula (5), taking, for example, 
H.M.S. "Heroine," which has been referred to by Mr Denny, I 
presume, as an example of the absurdity of my method of treating 
the question. The data for this is given in the last issue, ^'Sesults 
of trials made in Her Majesty's screw ships and vessels," as follows: — 



On Progressm Speed Trials. 
"Heroine," 7th September, 1882. 


; 1 
Trial Speeds, Revolutions, 


Power, 


(1) 13-12 

(2) 12-43 

(3) 11-47 

(4) 9-16 


113-2 

1081 

971 

76-2 


1466 

1243 

922 

471 



158 



>; s = 2-5 ; whence, 



The remaining necessary data are, d 
d's 
21 010 " — 1*1B81 ; and I calculate the quantity a — m = '081. 

Hence, 



Trial Speeds 

Multiplied by '081 = 
Add, Log N 
. ,, _ d's = 
^*^^ ^821,010 

Sum = 

Subtract from 
LogE, ;= 

Leaves value Log f - 

ue,, 
Morin's constant f = 


(1) 

13-12 


(2) 
12-43 


. (3) 
11-47 


916 


True 

Sjieed for 

(2)? 

12-51 


10627 

2-0638 

-1-1881 


1-0068 

2-0338 

-11881 


•9220 

1-9870 

- 1-1881 


•7420 

1-8820 

-M881 


1-0133 

2-0838 

-11881 


2*3046 
8-1661 


2-2287 
3-0945 


2-1044 
2-9647 


18121 
2-6730 


2-2362 
3-0945 


•8616 
727 


-8658 
7-34 


•8603 
7-25 


•8609 
7-26 


•8593 
7-27 



In- the foregoing each trial gives its own value and testimony to 

the truth of the mechanical principles involved in the equation, and 

the very exception shown by the slight excess of value in (2) is only 

an indication that the reported speed 12*43 for that trial is slightly 

erroneous, and that the data belong to the speed, 12-51 ! Thus, in 

the last column, taking this as the speed, we get f=:7-27 j same as 

ill 



154 



(M I^rogrssrive Speed Trialt. 



(1), while for (3) and (4) it comes out very slightly less, which is 

quite in accordance with Morin's deduction regarding this quantity, 

and borne out in the actual trials of the machinery of the ''Warrior'' 

and ^ Black Prince.'^ In confirmation of the speed of (2) being 

slightly underestimated, let us take the power and revolution for- 

mulaSy 

E = 8-56 V Log- 1 •OSS V; 

N = 7-65 V Log- 1 ^004 V. 
taking the speed 12*51, the calculation is as follows : — 
H.M.S. " Heroine."— Power Calcuktion. 



Trial Speeds = 

Vx-085 

LogV 

Log 8-56 = 

Sum Log E = 

/. E 

By trial = 


(1) j (2) 
13-12 1 12-51 


(3) 
11-47 


916 


1-1152 

1-1179 

•9328 


1-0684 

1-0973 

•9828 


•9750 

1-0596 

•9328 


•7786 
-9619 
9828 


81659 
1465 
1466 


8-0985 
1241 
1248 


2-9674 
927-7 
922 


2-6788 
471 
471 





Berolation Calculation. 




Trial Speeds 

Vx-004 
LogV 
Log 7-65 

Sum Log N 
•. N 
By Trial 




(1) 
18^12 


(2) 
12-51 


(8) 
11-47 


916 


-0525 

1-1179 

•8835 


•0500 

b0978 

•8835 


•0459 

1-0596 

-8835 

1-9890 
97-5 
97-1 


•0866 
•9619 
•8885 


s 


2-0539 
113-2 
113-2 


2-0808 
107-4 
108-1 


1-8820 
76-2 
76-2 

1 



On Progremve Speed Trials. 



155 



Let me ftirther illustrate the application of this formula (5) to the 
calculation of Morin's constant for the ''Merkara" and H.M.S. 
**' Shah," these being amongst the first vessels to which my methods 
were fully applied, and the firsts the vessel where Dr Fronde's method 
and mine came into collision. For the ^' Merkara " the trial data 
furnished by Mr Denny is published at the end of my ^'Letter of 
Redamation," where it will be seen, 

d>s 



a — n==*0756; also, Log 



21,010 



: — 1-6238. 



" Merkara." 



Trialspeeds = 

V X -0766 
LogK 

T *•«* 

^8 21,010 ~ 

Sum = 
Subtract from 
LogE 

Difference, Logfs 

• • 
Morin's const, f s 


(1) 
12-91 


(2) 
11-09 


(8) 
9-20 


(*) 
6^20 


9-16 


•9760 
1-8007 

-1-6288 


-8884 
1-7366 

- 1'6288 


•6955 
1-6672 

- 1'6238 


•4687 
1-4942 

-1-6238 


•6925 
1-6612 

-1-6288 


2-4006 
8-2896 


21978 
8 6881 


1^9705 
2-8661 


1-6867 
2-4757 


1-9676 
2-8661 


•8891 


-8908 


•8856 


-8890 


-8886 


7-746 


7-77 


7^685 


7-74 


7-74 



Here, agaiUi the slight variation of value in (3) may be seen to be 
due to the speed of (3) being slightly overstated: instead of 9*20 
knots it ought to be 910, and then all give practically the same 
value. 

Dr Froude, making use of the same equation I published in the 
spring of 1875, from (3) and (4) deduced the value f=10*04y which 



156 



On Progresswe Speed Trials. 



ifl rimply the reBuIt of an assomed fidse law of the resistance, masking 
the mechanical principle involved in Morin's constant. 
Again, for H.M. " Shah " we have, 

a — n= •0763; also, Log ^^Jj^ = 1-4161. 
H.M.S. "Shah.** 



Trial speedsT 

Vx-0768, 
LogN 

^ d«8 

^**« 21,010 

Sum 

LogE 

Difference, Log f 

• • 
Morin's constant f 




(1) 
16-45 


(2) 
12'13 


(3) 
8-01 


(4) 
5-32 


1-2551 

1-8152 

-4161 


•9255 

1-6573 

•4161 


•6112 

1-4729 

•4161 


-4058 

1-3034 

-4161 


8*4864 
3-8787 


2^9989 
3-8980 


2-6002 
2-8876 


2-1253 
2-5024 


8878 
2-440 


•3941 
2-478 


•8874 
2-440 


-3771 
2383 



These results are in fair agreement with my formulas, and it is 
thus shown how it is possible to calculate this quantity f by a defi- 
nite mathematical process ; but however carefully gone about, the 
observation of the quantities entering these equations, by their very 
nature involve causes of variation. For example, tidal and wind 
drift, residual errors of which are not properly eliminated by the 
usual methods of observation, and hence it is not at all surprising to 
find, that instead of ranging in straight lines, as when treated by the 
proper methods they ought to do, we find aberrations, such as those 
which seem to have peiplezed Mr Denny \ and in reference to the 
cases which Mr Denny refers in illustration, it can only be said that 
they display an evident tendency to rectitude, ^ /or (u Ma tn/t/'ym'- 



On Progresme Speed Triala. 167 

ties of human nature permit them. However, I am perfectly aware of, 
and have published explanations on some curious phenomena con- 
nected with discontinuity and changes of angularity in the lines 
in which the observation values range, which await fuller investiga- 
tion« Probably the most complete series of observations, upon the 
same vessel, ever published, were those conducted upon H.M.S. ''Iris/' 
The following table contains my deductions of the various co- 
efficients which enter my formulas, and the contrasted, calculated, 
and observation values of the power, revolution, and piston 
pressures for the different trials : — 



158 On Proffresrive Speed Triale. 

Power. 

E,. = 19-80 V log- 1-0830 V 
E„. = 21-00 V log- 1-0713 V 
En,. = 19-40 V log- 1 -0726 V 
E,y = 17-60 7 log- 1 -0733 7 

Bevolutions. 

N,. =5-08 V log- 1 -0020 7 
N„. « 6-72 V log- 1 — 0006 V 
N„,. = 4-545 V log- 1 -0083 V 
N,y. = 4-510 V log- 1 -0022 V 

Piston Pressures. 

(P+rp),. =3-957 log- 1-081 V 
(P + rp)„. » 3-827 log- 1 -0719 V 
(P + rp)„x. - 4-445 log- 1 -0692 V 
(P+ rp),y. =4-055 log-i -0711 V 



Trial Speeds 


Powers. 


BeToIotioiis. 


Pnsmms. 


V 


Formala. 


Trial. 


FormnU 


Trial. 


Formnla. 


TriaL 


16-58 


7608 


7503 


90-93 


91-04 


87-18 


85-86 


1512 


5251 


5251 


82-37 


82-15 


66-40 


66-57 


1206 


2384 


2560 T 


64-77 


6511 T 


37-52 


40-94 1 


819 


756 


755 


43-21 


43-86 


18-28 


18-14 


15-73 


4368 


4368 


87-96 


88-89 


6175 


51-18 


14-52 


8306 


3306 


81-34 


81-18 


42 35 


42-41 


11-58 


1628 


1637 


65-12 


65 07 


26-03 


26-21 


7-95 


616 


5711 


44-94 


45-05 


14-27 


13191 


18-57 


7996 


7714 


97-20 


97-19 


85 68 


82-68 


lC-56 


5100 


5108 


85-39 


85-39 


62-22 


62.31 


12-28 


1850 


1833 


61-28 


61-34 


3146 


31-13 


7-98 


587 


606 T 


38-54 


40-96? 


15-86 


15-41 


18-59 


7548 


7566 


9213 


93-25 


86-27 


84-40 


15-75 


3957 


8958 


76-96 


76-93 


53«36 


53-59 


12-48 


1803 


1765? 


59-95 


59-39 ? 


31-36 


30-95 1 


8-32 


596 


596 


39-16 


39-15 


16-87 


15'86 



On Progressive Speed Trials, 159 

Mr James Hamilton, jaa., said he would confine the few remarks 
he was about to make to subjects of general interest, as distinguished 
from the personal element in the matter before them ; for there were 
many important points connected with this paper which to him were 
of very much more interest than the conversations which took place 
in 1876, and which they had heard so much about. He thought it 
was a very good thing that Dr Froude's letter had been published 
in the Transactions. That letter would be the best defence that 
could be made for Dr Froude. As regards Mr ManseFs plotting 
down of curves, he had also plotted down a good many at different 
times, and he had found a good many straight and a good many 
crooked. He held in his hand a few, and it would be seen that one 
or two of them were very straight ; and there was one of them to 
which Mr Mansel had referred — that of the " Livadia," which took 
jumps. It required two parallel lines to represent it. 

Mr Mansel said he had brought that before the Institution, and 
showed it some time ago. 

Mr Hamilton replied that it might not be amiss to draw atten- 
tion to it again. He thought that this showed that if the lines were 
all as correct as that they might be better to call them curves. With 
reference to the initial friction, when those parallel lines were con- 
tinued to the origin, they found that about one-third of the power 
was absorbed by skin friction. There was another ship also, the 
^ Mendoza," that gave perfectly straight lines through all the five 
different points. The initial friction came to nearly one-third of 
the total indicated horse-power developed on trial, while on another 
occasion it came to about two-thirds of the indicated horse-power, 
leaving only one-third of the maximum power got out of the engines 
available for the propulsion of the vessel ; so that he thought there 
must be some better way of accounting for the loss. 

Mr W. Denny asked whether it was force or power ordinates he 
had made use of 1 

Mr Hamilton replied that he ought to have said that in the cases 
of the " Livadia " and the " Mendoza " that it was two-thirds and 
one-third respectively of the length of the ordinate representing the 



160 On Progremve Spud Tridt. 

gross indicated horse-power. Mr Mansel had referred to the '^ Iris" 
trials, and had mentioned that very capital experiments were made 
with the propellers. Since these experiments were made the 
'^ Phaeton '' had been tried, with the result of attaining much 
greater speed with the same horse-power, so that doubtless it was 
all owing to the difference of propellers. Now he ventured to think 
that if such differences in propellers occurred those differences would 
not be uniform throughout the curve, and that the propeller would 
be more efficient at one part of the curve than the other. He had 
not plotted down the " Phsoton's'' results, but all the information he 
had led him to believe that the results of the trials of the '' Iris" and 
the '< PhsBton" would show straight lines. Then it was known that 
the position of the wave produced by the vessel made a vast differ- 
ence in the resistance of the ship, and it was scarcely reasonable to 
think that those lines would be straight lines. As far as he could 
see they were straight lines when the vessels were of good form, and 
when requiring the ordinary indicated horse-power to propel them ; 
but when the ship was hard-pressed a much greater amount of power 
was absorbed outside of the useful effect produced with the conse- 
quences, that instead of straight lines they were crooked. He would 
like to refer to the diagram of the ^' Kangra." Mr Denny, in seek- 
ing to refute Mr Mansel's arguments, seemed to say— or at least 
he gave to him the impression— ^that the resistance was greatly 
made up of skin friction, as a general rule. He did not say what 
the speed was, and he would like to ask Mr Denny what the dimen- 
sions of the ship were, and the maximum power and speed got out 
of her, for at 14 knots, as given on the curve of the diagram, with 
the force there shown, the resistance appeared to be just about a 
half of what he was led to expect it to be, so that he must conclude 
that skin friction had very little to do with it. 

Mr Denny replied that the '^ Kangra" was a vessel of 285 feet in 
length, and by no means a sharp ship. On trial she attained a speed 
of not more than 12 knots, so that U knots were far beyond her 
capability of being driven with the power on board. 

Mr Hamilton said that this information demolished his argument 



On Prognmve Speed TriaU. 161 

altogether. He should like to refer to the question of wave forma- 
tion. To his mind it gave an indirect but a very complete confirma- 
tion of Dr Fronde's law of the corresponding speed. Mr Mansel 
had said that the idea belonged to Mr B^ch ; but be that as it maj, 
the confirmation of the law was very satisfactory and complete. A 
study of the diagrams before referred to would show that at difiEer- 
eut speeds there were different curves of wave formation, but it 
must be remembered that the one was from the model and the other 
from the actual trial of the vessel; and although they differed 
slightly, the correspondence was remarkably close. Now was that 
correspondence not a confirmation of Dr Froude's kw ? 

On the motion of Mr Henry Dyer, the further discussion of this 
paper was adjourned to next General Meeting of the Institution. 

The discussion of this paper was resumed on 24th February, 1885. 

Mr H£NRT Btier said— 

In resuming the discussion on Mr Denny's paper, it may be useful 
to the members if I explain in as brief a manner as possible, the 
basis of Mr Mansel's formulae, so that they may see how much they 
depend on general principles and how much on hypothesis. 

In treatises on engineering, there are generally three classes of 
formulae to be found. In the first class, an attempt is made to take 
into account all or nearly all the conditions of the problem, and 
thus expressions are obtained which are very complicated, and the 
application of which is very tedious ; in the second class, certain 
assumptions are made in order that we may simpUfy the resulting 
expressions, which are, however, exact enough for all practical pur- 
poses, within a considerable range of conditions, while, in the third 
class, by confining the applications to a limited range of conditions, 
we obtain the so-called empirical formulaB derived from experience. 
These three classes of formulae are well illustrated in the expressions 
for the efficiency of the steam in engines. If we attempt to take 
into aocomnt all the circumstances which affect that efficiency, we 

obtain expressions which fill several lines in an ordinary text book ; 

22 



163 On Progrutm Speed Trials. 

if we make certain aasamptions which experience proves lead to 
results which are not very far from exact we get expressions of 
manageable length; and lastly, if we assume data derived from 
ordinary practice, simple expressions are obtained which are ap- 
proximately correct within the limits of that practice. 

The question for us to consider is to which of those classes do Mr 
Mansel's formulie belong. When Mr Mansel first published his 
expression connecting the Indicated Power and the speed of a vessel, 
he obtained it by correcting the Admiralty formula, and in his papw* 
on '< Propositions on the Motion of Steam Vessels/' read before this 
Institution he says, '' it is not founded on any theory, but merely 
expresses the result of experiment on well designed vessels according 
to the practice of our best constructors," although in a later paper 
he shows that by making certain assumptions it may be derived from 
the principles of dynamics ; and he claims for it a much wider range 
of application than some of his critics are disposed to admit. His 
method of deducing the formnl» from theoretical considerations is 
somewhat abstract and difficult to follow by those who have not had 
a special training, so that I am afraid few have taken the trouble to 
find out the basis on- which his expressions rest. For a long time 
Mr Mansel has been kind enough to send me his papers, and some 
years ago I wrote a note to him from Japan suggesting how his 
formul» might be obtained in what I considered a comparatively 
simple manner, and which showed distinctly the assumptions he 
made, and how they affected the general application of his expres- 
sions. What I propose to say to-night is in great part a resume of 
what I then wrote. 

For convenience of comparison, I will use Mr Mansel's notation 
throughout. 

A steam vessel is a machine in which the energy exerted by the 
steam is spent in overcoming resistances, that is to say, in doing 
work, and it is subject to the same laws as other machines. Now. 



* Transactions of the Institution of fingineen and Shipbuilders in 
Scotland, Vol. XIX. 



On Progressive Speed TriaU. 163 

we know that the rate of doing yfork, or the quantity of work per- 
formed in a given interval of time by a machine is 

El = RV, (1) 

in which B is the resistance and V the velocity with which it is 
overcome. When E is expressed in the special unit of power 
nsnally adopted in engines, viz., 258,000 foot pounds per minute, 
then it is what is called the Horse Power of the engine. 

When we apply the expression to a steamship, and measure the 
resistance by the pull of a towing rope, when the ship is drawn along 
by an external force which does not interfere with the free flow of 
water past her hull, and if we denote by V the velocity correspond- 
ing to that resistance, then E gives what is usually called the Effective 
Horse Power of the engine. 
On the other hand, the Indicated Horse Power is 

E^-PV, (2) 

where P is the mean total effective pressure on the pistons, and V 
the mean piston speed. 

In the ordinary calculations relating to the propulsion of steam- 
ships, we want an expression which connects the Indicated Horse 
Power, which can be calculated from Indicator Diagrams, and the 
speed of the ship which can be ascertained from observations, so that 
if we multiply equation (1) by a factor involving the efficiencies of 
the mechanism of the engines, and of the propeller, we may then use 
it for expressing the Indicated Horse Power. This fact should be 
carefully noted so that we may see what is included in the constants 
of Mr Hansel's formulas. 
Differentiating equation (1) we have 





dE ^ ^, dR 




57=^ + ^5? 




E ^^dR 




= ? + ^57 




E/ 1 dR ' 


or if we write 






dR 




«= rfv 




"R 



164 On Pngrmive Sptei TfkUt. 

that is, 

we have 

IE; = T '^'*'*^- 

Integrating on the supposition that a is constant, we hare 

Loge E = Log, V + a V + const. ; 

or, putting the constant equal to Log 6, and using commou 

logarithms, 

LogE = LogV+aV + Log6 (3) 

Logy=aV + Logi, (3a) 

which is evidently the equation of a straight line 

Equation (3a) may be written in the form 

| = 6Log-iaV, (3b) 

or E = 6VLog-»aV, (3c) 

the factor Log - ^ oV denoting the number whose common logarithm 
is the product of « into the speed V, so that (3c) is the equation of 
a curve. 
Assuming 

^.(WM)» 
U~ 
where 

L = length of the ship, 

M ^ the immersed midship section, 

C = a constant, 
and substituting in equation (3), Mr Mansel obtains 

Log E = i Log (L VM)+Log V + ccV - Log C, (3d} 
or 

|Jii^»Log-«iV. (3c) 

Let us now consider the aasumptions which have been made. In 
the first phtce it has been assumed that 

dR -. 



On Frogremve Speed Triali. 166 

that is to say, in a vessel receiring a small increase of speed, the 
ratio of the increase of the resistance thus produced to the resist- 
ance, is equal to a small fraction of the increase of speed a being 
found from experience to be a small quantity varyiug in different 

vessels from .^ to -g, but constant so long as the conditions are the 
same. 

The second assumption is the expression for the value b, which is 
simply what Mr Mansel considers a corrected expression for the 

factor Q in the Admiralty formulad. 

How far these two assumptions are allowable must be determined 
from experience. Mr Mansel has shown by numerous examples that 
they hold within considerable limits. To use his own words on this 
subject, '^ the statement that the law of the power is expressed by 
equation (8d) must be understood in the sense that it expresses a 
hypothesis which is found to agree with the facts of experience when 
another implied condition is allowed for, namely, the special values 
of the quantities a and b which enter that equation are not the same 
for all speeds, they may remain constant through a great range of 
speeds, and then suddenly and simultaneously take other constant 
values through a wider range so that we may have two or three sets 
of values for the same vessel.^ Mr Mansel gives this as the result 
of his experience, and I must say I am not prepared in the meantime 
to explain why these sudden changes should take place. 1 would 
ask you to observe, however, that as £ in Mr Mansel's formula 
denotes the Indicated Horse Power that the constants are affected 
by the e£Qciencies both of the mechanism of the engines and of the 
propeller, so that it is possible to imagine two similar ships with 
different kinds of engines and propellers, having considerably different 
constants, as a variation in any one of those elements will produce a 
corresponding variation in the constants, and on the other hand, we 
might have two dissimilar ships with nearly the same constants, if 
the efficiencies of the engines and propeUers were different. 

I need scarcely explain that the word constant is here used not as 



166 On Prof^esrive Spesd Trials. 

signifying a qnantity which ia absolately constant, but simply one 
which is constant under giren conditions. 

Mr Denny, on the other hand, asserts that Mr ManseFs straight 
lines are the exceptions and not the rule, and are merely haphazard 
coincidences. The discussion of how far Mr Mansel's formula give 
results, agreeing with experience, I should like to leave to those 
members who are actually engaged in shipbuilding. 

I think it is probable that the majority will agree with the 
opinion expressed by Mr Hamilton at the last meeting when he said 
that '^ as far as he could see the lines were straight when the vessels 
were of good form, and when requiring the ordinary indicated horse 
power to propel them ; but when the ship was hard-pressed a much 
greater amount of power was absorbed outside of the useful effect 
produced, with the consequences that instead of straight lines they 
were crooked,'' and I do not think, at least, so far as I understand 
him, that Mr Mansel claims more for his formulse. 

Mr Hamilton further remarked, 'Hhat it was known that the 
position of the wave produced by the vessel made a vast difference in 
the resistance of the ship, and it was scarcely reasonable to think 
that those lines would be straight lines." That may be admitted, but 
still, as I have already pointed out, this increase of resistance might 
so affect the efficiencies of the engines and of the propellers as to 
correct in great measure the deviation from straightness of the line 
of indicated horse power. However, this is a point which can only 
be settled by further experiment. 

With regard to the shape of the formulae, I would remark that 
the use of logarithms leads to the easy construction of a straight 
line, but as Mr Froude has noticed in his letter to Mr Mansel, a 
given alteration of the pressure ordinates, produces a less and less 
alteration in the corresponding logarithmic ordinates, so that 
although the logarithmic form may be more convenient for purposes 
of practical calculation, an expression not involving the use of 
logarithms might be preferable for purposes of investigation. 

The only other point in the discussion, between Mr Mansel and Mr 
Denny, which I will touch, is the method of obtaining the initial 



On Progressive Speed Trials, 167 

friction of the engines, but which I prefer to call the pressure 
necessary to work the engines unloaded. 

The Indicated Horse Power of an engine is expressed in terms of 
the mean effective pressure of the steam, the length of the stroke, 
the diameter of the piston, and the number of revolutions per 
mmnte by the formula. 

I H P -: P 2n J a^s ^ T ncPs u) 

33,000 "^^Q 
for a compound engine with two cylinders, Mr Mansel writes this 
in the form 

I.H.P. = ^,(P+^) (^a) 

where P and p are the respective mean pressures on the small and 
large pistons, and r the ratio of the greater to that of the smaller 

piston. As the quantities in the factor st-qi a remain constant for 
a given speed we may write 

I.H.P. = C(P + fp), 
if we denote by m the pressure necessary to overcome the friction of 
the engines, we have the power delivered to the crank shaft 

= C (P + r/?-m), 

and this is equal to the effective horse power, multiplied by a factor 

n H 
of the form -^ where H is the pitch of the screw in feet, and n 

the number of revolutions per minute, from which we deduce Mr 

ManseFs expression, 

V2 = C(P + r/?-m), 

which, however, he derives in a similar manner to the equation to 
the power, that is by correcting the Admiralty formula. He calcu- 
lates the numerical values m from two experiments at moderate 
speeds, by eliminating C between the two values of the equation 
thus obtained. In doing this he makes two assumptions; in the first 
place, that C is absolutely constant, and also that m remains the 
same not only for the two trial velocities, but also down to zero 
velocity, two assumptions which may give approximations to the 
truth, but which cannot be regarded as exact. 



168 On Progrttme Speed Triab. 

On the other hand, I agree with Mr Denny when he Bays he does 

not think it possible to arrive at an exact quantitative measure of 
the initial friction by means of Mr Fronde's method, as I am of 
opinion that the only data of any value of this subject are tiiose 
obtained from actual experiments with steam engines. 

It will be observed that Mr Mansel's expressions belong to the 
second class of formul» which I mentioned at the beginning of my 
remarks, as they do not take into account all the varjring conditions 
of the problem, but are simplified by certain hypotheses which Mr 
Mansel considers justified by experience. To*night, I have confined 
myself to showing the basis on which they rest^ and the assumptions 
made with a view to simplifying them, so that these latter may be 
discussed by members who have had opportunities of applying the 
formulsB in practice, and I have not entered into the general question 
of steamship propulsion, which would require a special paper for 
itself. 

For the further successful prosecution of the various subjects^ 
raised by Messrs Mansel and Denny, we want many more experi> 
ments, not only with models, but also with actual ships and engines, 
and I trust that those members of the Institution who have oppor- 
tunities of making them will do so, and publish some of the results 
in the Transactions, in order that those of a more mathematical turn 
of mind may find out either how Mr Mansel's formulae may be 
improved, or better ones put in their place. 

Mr Qeoroe Thomson said — 

The remarks made by Mr Dyer are possibly pretty scientific, but, 
Mr Mansel in opening the discussion of Mr Denny's paper has^ I 
think, brought into play his well-known abilities. We most all 
admire a gentleman like Mr Mansel, who has devoted so much of his 
time, so assiduously, during the last 85 years, to the study of steam- 
ship propulsion. 

The figured data he has put before us, explanatory of his investi- 
gations, is of great practical value, and convey more to my min d 
than the zig-zag lines Mr Denny has shown up to us, as the 
exponents of the principles Mr Mansel advances. 



On Progressive Speed Trials. 160 

Model experiments may be very good, only, we are distinctly 
told that these model experiments are supplemented by the results 
of trial data from known ships. Theoretically then, Mr Denny 
makes up a ship's horse power, plus some intangible quantities, but 
like every practical and sensible shipbuilder, retreats to practical 
deductions from known facts, and draws his inference therefrom. * 

Mr Mansel's object has been to simplify, as far as I can see, our 
mode of procedure, by bringing all the results to one constant, 
instead of having so many conflicting co^efficients, and there is no 
disputing that this must be of great advantage. 

In the last issue we have the results of the trial of H.M.S. " Iris," 
and applying Mr Ma9sers formula in the 4th series of trials we have 
7543 I«H.P., for a speed of 18*59 knots; supposing we wanted that 
speed with the 1st set of propellers, we would have to expend 
12,525 I.H.P. or 66 per cent, more power for the same speed; this 
fact agrees very closely with results I plotted on the same vessel 
some months ago, and my conclusion is, that we have a prodigious 
hump to get over here, in which the bow spray and minikin waves 
sink into insignificance in Mr Denny's illustrations. 

Hollow wave formation in the vicinity of paddle wheels and the 
waste of power caused from that source is a tradition of long stand- 
ing; it was pointed out to me by draughtsmen who have studied 
marine painting many years ago. It will he my endeavour to get 
the results of resistance reduced to straight lines or fair curves, 
rather than pursue a policy of humps and hollows. We have got 
torpedo boat humps in the craft referred to in Mr Denny's paper, at 
19 knots 365 I.H.P. 
19-5 „ 402 „ 
20-0 „ 425 „ 
We get here from 19 to 19-5 knots at the expense of 37 H.P., and 
the next half knot so cheap as 23 h.p. Now, I believe, the observa- 
tions for this craft were taken as near as was possible, but practical 
people will put the 37 horse power to the opposite side, and we are 
not yet bo credulous as to accept without a doubt^ that a boat 

could spin for us exactly 17, 17*5, 19, 19*5, and 20 knots, as the 

23 



170 On Frogresske Speed Triais. 

data shows. Those who have studied the diagrams in connectioB 
with this boat must admit not only the difficulties of taking correct 
cards at so high velocities of the piston, but also the true mean 
pressure from them. Mr Denny's progressive methods of trial have 
thrown a flood of light on erroneous theories, but in actual practice I 
think it best for every man to use his own ways, although if time 
allowed to try the modes of others for comparison; these must^ how- 
ever, be like Mr Mansel's descriptive ship, "sl)ort and handy." 1 
have often looked at the S.S. ''Merkara's" power and speed curve 
compared with a simple curve of logarithms, but it is the only ship's 
curve I have seen follow this law so closely, and have merely 
brought this matter up to make people cautious in accepting 
formulae unless thoroughly investigated, this, of course, just being a 
partial coincidence. Making the base of the logarithm 100 = speed 
we have 

899 = 6 knots. 
818 = 9-12 „ 

1325 = 11-22 „ 

2048 = 13-11 „ 
then deducting 100, which I made the base, from these results, we 
have the horse powers of the "Merkara" with a wonderfully good 
approximation to her trial speeds, and it is clearly seen that if I 
put off abcissse representing these speeds in logarithms and thib 
horse power plus 100, 1 have a straight line, in fact for a logarithm 
pure and simple, the angle of 45 degrees, 

I quite agree with Mr Denny that there is no defined limit to the 
speed of any vessel if force enough is put into her to gain it, but 
the speed wanted may bo got at great cost An engine and pro- 
peller have, however, as is too well-known, a limit in their 
capabilities, above the maximum capability, no more speed is got. 
There is also another point to keep in view, and that is the minimum 
ability of the engine to keep up constant momentum of the pro- 
peller without making intervals. This will give a speed below which 
the ship cannot be driven with the engine in steady motion, I would 



On Progressive Speed Trials, 171 

call this initial speed, and these first impulses hare a great deal to 
do with after effect. 

Until a thorough analysis is made on screw propellers, and their 
actual values as propellers elucidated, it appears futile to deal with 
anything but real data deduced from actual trial with known 
qualities of the ship and propeller results. 

Supposing I ask a scientific gentleman what horse power it will 
take to drive a vessel 16 knots an hour, giving him particulars of 
displacement^ &c., but at the same time I bolt on a couple of stout 
flat plates for blades on the boss for a propeller ; getting round on 
trial trip as if disappointed with the result of speed, I ask my friend 
what he was thinking about in leading me to understand the speed 
would be no less with so much horse power. 

As soon as Mr Mansel and Mr Denny are prepared to solve the 
propeller difiiculty, it will be time enough for us to adopt their ways 
and means of saying a certain horse power will make a ship go so 
many knots per hour. 



172 



On Progressive Spud Triah. 



Cnrve of Common Logarithms 8ho\?mg Close Approximation of 
" Merkara's " Speed and Power. (Referred to by Mr G. Thomson.) 




On Progressive Speed Trials. 173 

Professor Elgak said that he did not mean to refer to the 
personal questions which were involved in the subject of the paper 
that had been read, except to say that personal questions were 
perhaps not always without advantage to the interests of a scientific 
institution. They were sometimes the means of attracting attention 
towards points which might otherwise be regarded with comparative 
indifference ; and they sometimes gave to technical discussions an 
interest and thoroughness which they would not otherwise possess. 
In this case the personal discussion, which had been raised by Mr 
Hansel, had had the effect of eliciting from Mr Denny some extremely 
interesting information, relating to model experiments and progres- 
sive speed trials. A large quantity of useful data had thus been 
furnished, which would make the volume of Transactions of the 
Institution for the present year exceedingly valuable to naval 
architects. They had also obtained, from Mr Mansel, a great many 
instructive examples of the application of his method of estimating 
the speed of ships. Mr Dyer had that evening given to the 
meeting a dear and concise explanation of the principles upon 
which Mr Mansel's methods of calculation are based. He had 
not been quite clear, before, whether Mr Mansel put his system 
forward as an empirical mode of describing facts and predicting 
results ; or whether he claimed for it mathematical accuracy. He 
gathered, from what Mr Dyer had just said, that what is claimed 
for Mr ManseVs method is, that it is mathematically exact, provided 
certain conditions are fulfilled ; but that those conditions are them- 
selves subject to variation according to circumstances. The precise 
circumstances which cause such variation, and the possible limits of 
variation, can only be decided by experimental trials. That being 
so, some' of the irregularities in the curves produced by Mr Denny 
to show that Mr Mansel's method does not always give straight 
lines, may very well be accounted for. At the same time he would 
not be surprised if, as Mr Mansel pointed out in the discussion, 
some of the departures from straightness arose from errors of obser- 
vation in recording the results of the speed trials, and from the 
conditions not being absolutely perfec One of the most astonish- 



1 74 On Progressive Speed Trials. 

ing results of the discussion upon Mr Denny's paper, to him, is that 
Mr Mansel should have contested, in the terms he did, the propriety 
or fairness of calling the law of comparison, which is so intimately 
associated with Mr Froude's name, Froude's law. Mr Mansel spoke 
of M. B^h's labours in the same direction, and of the British 
Association Report which referred to them; and he asserted that 
M. B^ch first discovered and established the law of comparison. 
He (Professor Elgar) was aware that M. B^ech many years ago 
deduced this law by strict mathematical reasoning from a theorem 
of Newton's. Bach's investigation was published in one of his 
scientific works, but no one appears to have considered it of any 
practical importance, or of more than abstract interest. No use 
was made of it, even in France, so far as he was aware, and it 
was apparently never submitted to experiment. Certainly, no one 
in this country knew anything of, or believed in the existence of, 
such a general law. Professor Macquom Bankine— who knew as 
much of the science of the subject, and of what had been proved 
with reference to the laws of resistance, as any one — said at the 
Institution of Naval Architects in 1864 — ^' As for mis-shapen and 
ill-proportioned vessels, there does not exist any theory capable of 
giving their resistance by previous computation.'' Professor Bankine 
could not have said this had the law of comparison been completely 
established and proved — ^as it was later on by Mr Froude — ^to be 
applicable to the purpose. That was in 1864, and the report of the 
British Association Committee in 1869, upon which were Professor 
Bankine, Mr C. W. Merrifield, and Mr Froude, states— '^lliere 
exists no generally recognised theory or rule for calculating the 
resistance of a ship." Where was the law of comparison which we 
are now told had long before been clearly demonstrated and made 
available by B^ch 1 B^h may have described it as a theoretical 
deduction from a dynamical theorem, and may have expressed it in 
that form; but the law was not proved, nor supposed to furnish a 
practical means by which the resistance of ships might be determined, 
from the observed resistance of models. It certainly was believed in 
by no one. In the year 1869, Mr Froude first publicly propounded 



On Progressive Speed Trials, 175 

the general law of comparison, which bears his name, in its broad 
and general form, in the Appendix to the British Association 
Beport. He (Professor Elgar) can well remember Mr Merrifield 
reading a paper before the Institution of Naval Architects in 1870, 
in which it was intimated that Mr Froude was about to experiment 
on models, for the information of the Admiralty, in order to 
ascertain what results might be obtained by applying the law of com- 
parison. Few thought that this would do more than give a little 
innocent amusement to those who were interested in such matters. 
Mr Merrifield said — ''The present theory is that the velocities 
should vary as the square roots of the lineal dimensions when the 
resistance of vessels of different sizes is to be compared; there is 
reason to beUeve that the comparison under these conditions very 
fairly represents the facts, but we are at present very far from 
knowing how much this law approaches to the truth, or what are its 
limitations." Now, these remarks fairly represent the state of 
knowledge in this country upon the subject, when Mr Froude was 
yet in the early stages of his model experiments. Mr Scott Hussell, 
who had probably done more than any one else in that direction, 
remarked that '^ he must prepare the meeting not to expect reliable 
results from experiments with small models. He had once made a 
series of experiments with 120 small models, extending in one 
instance from 24 inches to 12 feet in length, and in another from 30 
feet to 60 feet in length, and the most interesting fact he ascertained 
was that the results upon a large scale were precisely contrary to the 
results on a small scale." How can it now be said with justice that 
Mr Fronde's work had been done years before by B^ech, and that 
the truth of the law of comparison had been established. Now, he 
did not think it right, nor fair to the memory of Mr Froude, 
considering that the state of knowledge of the subject, when he 
took up this difficult and complicated problem, was as thus de- 
scribed, to say that he borrowed a law already proved by E^ech, 
and that "Etch's hypothesis is strictly the one which under the 
name of Fronde's law has been much lauded in recent years." Mr 
Mansel makes a charge either of plagiarism or of unconscious imitia- 



176 On Proffressm Spe^d Tfj/ois. 

tion against Mr Fronde 1 He did not suppose for a moment that Mr 
Mansel really believed that Mr Froude had been guilty of plagiarism. 
A great many of those present had had the honour of knowing Mr 
Froude, and they were perfectly satisfied that he would be one of the 
last men in the world to deck himself in borrowed plumes. The 
idea is absurd in connection with such a man as the late Mr Froude. 
No one was ever more modest than Mr Froude in valuing, or claim- 
ing credit for, his work; or was more generous in according merit to 
others, or in acknowledging any assistance he might derive from the 
labours of others. If such a charge were made no one who knew Mr 
Froude would consider that a serious reply to it was necessary. Bat 
he also considered they might confidently say that Mr Froude did 
not even unconsciously imitate R^ech. The work of the two men 
was entirely dififerent, and although, up to a certain point and 
in one important respect, the results arrived at were similar, it 
must be remembered that these results were obtained by totally 
diflferent modes of reasoning and research — Btech, by pure mathe- 
matical deduction from an abstract dynamical theorem; and Mr 
Froude, by means of the modem stream-line theory, derived the 
same general law. It is quite certain that Mr Froude had no 
knowledge of what R6ech had long before published. But the 
theoretical proof of the law was but a step towards a practical 
comparison of the speeds of models and of ships. The law does not 
hold good for the gross amount of resistance, as Beech appears to 
have assumed it would practically do. It applies to certain elements 
of resistance, but not to others. The law was not applicable to any 
useftil practical purpose until the gross resistance had been resolved 
into its principal component elements : and until those elements had 
been eliminated and separately investigated which do not conform to 
the law. The reason why Mr Froude's name is better known in con- 
nection with the law or scale of comparison than M. Beech's, is 
because of the way in which— after first of all deriving it firom the 
the stream line theory — he fitted it for, and brought it into, success- 
ful practical use ; and on account of the ingenious and exhaustive 
manner in which he analysed the different elements of resistance, 



On Progressive Speed Trials, 177 

separating those to which the law rigidly applies from those to 
which it does not. Mr Fronde proved the truth of the law of 
comparison, and the conditions under which it holds good ; and he 
discovered and defined its limitations by means of a wonderful com- 
bination of theory and experiment. I sincerely trust that the effect 
of this discussion will not be to leave an impression upon the mind 
of any one, that Mr Froude's memory does not deserve all the 
respect and honour that an Institution of Shipbuilders and Engineers 
such as this can possibly pay to it. 

Mr Biles said that Mr Denny had kindly referred to some work 
in which he had engaged in regard to the speed of ships. He would 
like to endorse what Professor Elgar had said with regard to Froude's 
law of comparison. He believed those who had studied Froude's 
writings must know quite well that he would not have attempted to 
detract in the slightest degree from the merits of any one's discovery. 
He tliought that this law of comparison, valuable as it was, was a 
very simple deduction from a well-known theorem, so that there 
was very little merit in its discovery, but much in its application to 
the question of the resistance of ships. It might, however, be said 
that until Fronde applied this law, the question of the speed of ships 
was not a law at all; and it was only because of the careful 
experiments he carried out that they had been able to make the 
slightest step in advance in that matter. With regard to the ques- 
tion of speed trials, as he understood the method that Mr Mansel 
claimed — that the usual friction produced the straight lines. Now, 
he had had some experience in steamer trials, and he must say he had 
had great difficulty in getting true results at low speeds. Would 
Mr Mansel inform them what kind of springs he had used in his 
indicators 1 Then there were other causes of error which might come 
into the question of speed trials, especially at the measured mile on 
the Clyde, at Skelmorlie. Two runs on the mile distance there was 
considered enough to determine the true speed of a ship. That 
might be correct in high speeds, although there were several things 

might come in to disturb them — such as the state of the tide, the 

24 



178 Oih Progressive Speed triak. 

time of the moon, and also variations of distance from the shore 
where the vessel was ranning— all matters difficult to eliminate 
from the fasts of the case in two runs on a mile. But when the 
trials were at low speed, with a 5000-ton ship, and a force of 200 or 
800 indicated horsepower propelling her at foor or five knots, the 
forces that might come in to cause variations were considerably 
greater than the force that was necessary to propel her; and 
therefore it was most difficult to ascertain the power that was 
required to drive a ship at low speeds. In order to get clear of 
these difficulties, he suggested that in trials of a ship's speed they 
ought to take a few speeds at the mile distance, and then they coold 
run straight ahead down the Frith and take a close series of revela- 
tions and indicator cards. Or they might use the method which 
had been employed on the Clyde before now — the Dutchman's log. 
If that were done for a few ships, the difficulty of getting the true 
power at low speeds would become apparent, and it would be a good 
step towards finding a method for obtaining the true power of ships 
at low speed. He therefore recommended the running of a vessel 
a greater number of times at low speed in order to throw some 
light upon this question and upon the accuracy of Mr Mansel's 
law. Froude's reply to Mr Mansel had — ^as far as he could under- 
stand it, and as far as he understood Mr Mansel's paper — raised 
difficulties which it was impossible to forget. That question of the 
mathematical analysis of the curve at the lowest point seemed to 
him to be fatal to Mr Mansel's law. 

Mr Wh. Dennt, in reply, said he thought Mr Dyer had put into 
a very neat form the variation of thrust with variation of speed 
necessary for the production of a straight line. Beyond this he 
did not pretend to state a priori the grounds of the straight line 
theory. In any case he thought Mr Dyer had given good 
advice to this Institution, in asking the members of it to do 
all in their power to produce a large amount of accurate experimental 
data bearing on the subject As he had very correctly remarked, 
such data formed the foundation on which alone theory could be 



On Progressive Speed Irials. 179 

[ffoperly msed. Mr Dyer had made reference to a remark of Mr 
Hamilton's— that he had found the lines to be straight in vessels 
of good form, when requiring the ordinary indicated Jhorso-power 
to propel them i but to become crooked when the ship was hard- 
pressed. He (Mi Denny) was not cognisant of the data, or the 
extent of the data, from which Mr Hamilton had deduced this idea ; 
but it would require a very considerable amount of data to prove 
his statement Mr George Thomson — whose voice he was glad to 
hear that night as an old pupil of his own — had stated his preference 
for straight lines, and he thought that in that preference everyone 
present would concur. Had Nature favoured them with straight 
lines they would all have been happier, and the problem would have 
been easier to solve; but instead of facility Nature had given them 
such difficulty as would draw out what was best in them. Professor 
Elgar, in some of his remarks, had anticipated some things which 
he intended to say in reference to Mr Mansel's argument ; but he 
would not hesitate to repeat them, because he had taken some 
trouble to set them forth with perhaps more completeness than 
Professor Elgar had been able to do, from a short study of the 
subject, and he was quite sure they would forgive him for reiteration 
in this matter. Mr Biles' remarks about the difficulties of obtaining 
accurate results in speed trials at low speeds were very important. 
He could only blame him for his modesty in not taking the credit to 
himself for inventing the method of trial which he had suggested to 
them. That method was gaining ground among experimenting firms 
on the Clyde. It was by no means a difficult method ; and it had 
the advantage of being applicable without serious inconvenience in 
cases where it was not possible to carry out fully measured mile 
triab with a steamer. Mr Denny then went on to say — In 
Mr Mansel's reply, I observe, he repeats his assertion that I have 
charged him with plagiarism. I therefore repeat, that I have 
not charged him with plagiarism. My position regarding his 
relationship to Mr Froude is clearly stated at the foot of the second 
page of the paper I lately read to you. There I said that " At the 
time I made the statements which Mr. Mansel has quoted, I was 
under the impression that the idea which I conveyed to him had 



180 On Progressive Speed Trials 

lain in his mind, and was the seed from which germinated his 
method of dealing with the initial firiction. I distinctly pointed 
out in the remarks quoted by Mr Mansel that I believed this was 
an unconscious stimulation of his mind. I am afraid Mr Mausel is 
so sensitive about such questions that he is apt to fsdl into similar 
misconceptions, as, for instance, in the few remarks he made at the 
end of my paper. He there says : " He would like, however, to 
notice one statement in the paper, where Mr Denny says— 'I think 
it well to say a few words upon the analysis of power with which 
Mr Mansel, nine and arhalf years ago, started his discussion of my 
progressive trial data.' He thought Mr Denny was here assuming 
rather much credit to himself, since long before the time referred to 
he had worked at such matters." This remark of Mr Mansel's could 
only have been justified by my having said that he started this 
analysis of power at the discussion of my progressive trial data, 
instead of, as I did say, that he started the discussion with this 
analysis of power. Such misunderstandings offer both opportunity 
and temptation for the employment of i^antcr rather than reasoning 
in replying to them. It is not, however, my purpose to employ any 
such methods in these remarks, but rather to do all in my power to 
set before you as fairly and impartially as I can an answer to Mr 
Mauscl's reply ; and I am all the more anxious to do so, as I have 
resolved that this shall be my final answer to Mr Mansel on this 
subject. I have taken much care to study the points raised by him 
in his Letter of Reclamation, and consider that he now receives from 
me all the satisfaction it is within my power to give, or that he 
has any right to claim. On the question of priority I have nothing 
further to add to what I have already said, as neither in my own 
researches, nor in the reply of Mr Mansel, has anything come to 
light calling for further remark. The letter quoted by him has no 
bearing on the question, as it is of date 4th December, 1875 ; while 
the conversation between us described by him occurred in the 
autumn of the same year. Mr Millar, it will be observed, has drawn 
attention to the date of this letter in a foot-note, and on the 9th 
inst., previous to the final correction of his proofs, I wrote Mr 
Mansel, drawing his attention to the date. 



On Progressive Speed Trials. 181 

Tnrning from the personal question to the scientific aspect of this 
discussion, I regret Mr Mansel has been unable to appreciate the facts 
which I have brought forward regarding his logarithmic lines. In 
order to help him in this, I now show the logarithmic lines of the 30 
trials, furnished by my firm, extended upon three supplementary dia- 
grams (see Figs. 13, U, 15, Plates XIV., XV., XVI.), with a straight 
line under each. In addition, all the four spot trials of the Admiralty 
vessels, previously referred to, have been grouped in another sheet, 
(Fig. 13, Plate XIII.), and treated in the same way. Regarding my 
firm's trials, please note that owing to some mistake three of them 
do not fulfil completely the conditions laid down, viz. : that they 
should all be trials having four spots, and with the propeller com- 
pletely immersed. These three errors are noted on the diagrams, 
but they do not affect the general question. You have only to look 
at the four diagrams to see that straight lines are exceptions and not 
the rule. In my paper, I said that Mr ManseFs method, instead of 
universality, had only the character of occasional fitness. Even 
this occasional fitness can be explained in a very simple way. I 
show a diagram, (Fig. 17, Plate XVIL), giving the resistance curve 
deduced from model experiments of the '* Manora ' set off logarith- 
mically the same as already exhibited on Fig. 7, Plate VIII. You will 
observe this is a very wavy curve, and yet that it is possible to draw 
through it a straight line cutting it in six different points. Supposing 
that on the trial of this steamer you had happened to hit upon these six 
different points you would have felt you had very fair justification in 
saying that the " Manora's " resistance curve set off logarithmically 
formed a straight line. But it is not very likely you would hit upon 
these six spots, the probability being that your measured mile trial 
had only supplied you with four spots. With four^pots, especially if 
you allow yourself the privilege of rejecting one of the four as 
incorrect, you have a certain reasonable possibility of getting a 
straight line. If the irregular spot occurred on the top of one of the 
humps, then this rejected spot instead of being erroneous would be 
really the only one giving you a hint as to the true nature of the curve 
with which you were dealing. With three measured mile spots the 



182 On Progresdve Speed Triak, 

possibility of getting a straight line is still farther increased, and if 
two spots only are obtained, which Mr Mansel at one time con- 
sidered quite sufficient, the possibility becomes a certainty. I believe, 
even among the straight Jines obtained, the foregoing explanation 
holds good with regard to very many of them. Measured mile pro- 
gressive trials at the best are, in the number of spots, very imperfect 
and quite inadequate to form the foundation for such a broad theory 
as Mr Mansel has embodied in his three laws of the revolutions, the 
pressures, and the gross power. In a mass of voluminous figures, 
Mr Mansel shows some cases of agreement between his formula and 
the results of experience occurring among the large number of cases 
he has analysed. Even, however, in these selected cases exceptions 
occur which have to be summarily dismissed as due to errors in 
observation or other causes not likely to conflict with the theory. 

At our last meeting, Mr Mansel again pressed upon you the value 
of his method as affording a standard by which the accuracy of all 
measured mile trials could be judged. I do not think you will 
endorse such a recommendation, or be prepared to admit that 
scientific laws are dependent upon exceptions instead of upon 
generalised facts to which there are either no exceptions, or to which 
the exceptions are completely and satisfactorily explained. But Mr 
Mansel asks you to do more than this, and to make a theory the test 
of practice when that theory is still upon its trial. He asks you to 
stretch or shorten every ordinate which does not agree with his 
formula, and the same reasoning will oblige you to go even further 
and to reject every trial which produces curved or irregular loga- 
rithmic lines, and to condemn all model experiments because thej 
show clearly that the resistance does not vary as it ought to do if a 
straight line is to be produced. This is not science but dogmatism 
—a dogma being an opinion which demands the unreasoning rejec- 
tion of every opinion and fact which may prove contrary to it. 
- Mr Mansel objects to my having, in my Watt lecture of 
January, 1882, upon the speed and carrying of screw steamers, 
given Mr Froude the honour of the law of comparison in having 
called it by his name. He says : ^' This is exactly what Btech 



On Progressive Speed Trials. 188 

dedaced some fifty years before." And he further says : " It 
seems to me those statements are not fair towards the memory of 
M. B^h, and very iigadicious towards that of Dr. Fronde/' I 
wish to do justice to the memory of B^h, for I very greatly 
esteem the services which that distinguished Frenchman has ren- 
deredy not only to naval architecture, but to science in general. 
As to my statement having been injudicious to the memory of Mr 
Froude, I think I shall be able to show that while E^ech, at an 
earUer period, stated the theory of comparison, he did so only as 
a theory. He did not pretend to establish the law by experiment, 
in which case he would have found that the skin friction did not 
follow the law, but required a separate experimental and analytic 
investigation. Stoch died last year, were he still alive I should 
have taken the opportunity of consulting him personally upon the 
matter ; but having the pleasure of knowing M. Jules Chaudoye, 
a distinguished member of the constructive staff of the French Ad- 
miralty, and a late pupil and friend of M. B^ch, I took the oppor- 
tunity, when last week in Paris, to ask him if he knew in what light 
S&ech regarded the work of Mr Froude. M. Chaudoye told me 
that B^h, while not personally knowing Mr Froude, had a very 
great admiration for his work, and that he (M. Chaudoye; had 
had never heard him speak of Mr Froude in other than terms of 
appreciation. Such are not the feelings of an injured man towards 
the person who has done him injury. There is no doubt B^ch, in 
his book entitled ""Cours de M^canique," published in 1852, 
enunciated in a broad theoretical way the law of comparison, and I 
think this Institution owes Mr Mansel its thanks for having drawn 
attention to this matter. Before he mentioned it I was ignorant of 
what B&ech had written upon this point. Since our last meeting I 
have examined Beech's investigation, and I am glad to have done 
80 because, in the British Association Beport, the reference to B^ech 
seems to be based on a misunderstanding of his work. In that 
report it is stated that B^h's conclusion ^'would follow from the 
theory of the resistance of submei^d bodies, on the supposition 
that the resistance varies as the square of the speed.'' But the case 



184 On Progressive Sj)ecd Trials. 

of a submerged body is not a good basis for the law of comparison, 
which is strictly appropriate only to wave-making resistance. In a 
submerged body this element of resistance is wanting. 

Even in Mr White's " Manual of Naval Architecture," published 
in 1882, as great a misconception exists regarding Reech's 
reasoning. On this account I am adding, in the appendix, a transla- 
tion of the chapter in the '< Cours de M^canique/' which deals 
with the law of comparison. In printing this translation, I am 
compelled to notice that in some ^points^Beech had not arrived at 
correct ideas, and that some of his statements must be admitted to 
be erroneous. These points do not, however, impair the validity of 
his fundamental reasoning and conclusion. A. careful study of R^ech's 
work, and a comparison with the late Mr Fronde's published &ad 
unpublished papers, show that these two men arrived at their con- 
clusions by quite different methods. It is evident that Btech 
demonstrated his theory on abstract dynamical principles, basing 
it on the theory of similarity, as laid down by Newton. He 
acknowledges his great indebtedness to Newton, and as I had 
the pleasure of seeing in M. Jules Gbaudoye's written notes of 
his lectures, he also acknowledges his indebtedness to Joseph 
Bertrand, the eminent French mathematician, who he declares 
first brought this theory of Newton into prominence. It is exceed- 
ingly interesting to note how this great thinker delights in acknow- 
ledging his indebtedness to the suggestions of other minds. We 
find the same spirit equally developed and evident in the late Mr 
Froude. Even from the rider to the British Association Beport, 
this feature in Mr Fronde's character is very apparent, as he men- 
tions several times his indebtedness to Bankine. 

I may point out that this British Association- Report was pre- 
pared by the late Mr C. W. Merrifield. It was submitted as a 
draft to Mr Froude, and signed by him '' subject to explanations." 
It is not, therefore, to be assumed that Mr Froude studied the 
original writings of all the foreign authors named in it« Indeed, it 
is evident from the rider that he trusted to Mr Merrifield for the 
correctness of these references. In this rider Mr Froude very clearly 



On Progressive Speed Trials, 185 

points oat that he had based those researches which led him up to 
the law of comparison apon Bankine's stream line theory, and 
acknowledges that theory as the source from which he drew the law. 
From the mistaken way in which K^ech's theory is put forward in 
the British Association Report^ it is very probable that Mr Froude 
passed it over as based upon an erroneous assumption, which^ in his 
ignorance of Koch's actual work, he would be entitled to do. It must 
be clear to you that these two distinguished men arrived at the idea 
of the law of comparison by different roads. In so far they were dis- 
aimilar, but in the generosity with which they acknowledged their 
indebtedness to their great teachers they were alike. But, admitting 
the principle of comparison to have been enunciated as a theory, and 
granting to R^ech the priority of such an enunciation, just as Mr 
Froude would have done, had he now been among us, we must admit 
that much labour would have to be put forth in experiment and 
analysis before such a theory could be raised to the security of a law. 
Any physical law which is to be counted of established and per- 
manent value must not merely originate in theory, but be verified 
and confirmed by experiments. It is the doing of this work in 
addition to the independent origination of th6 theory which entitles 
Mr Froude to have his name permanently attached to this law. It is 
not irrelevant to remind you that by Newton's own acknowledgment 
the three laws which bear his name were understood before he 
formulated them and built them into the magnificent edifice of the 
Principia. 

To establish the law of comparison, the total resistance has to 
be analysed into its separate elements, which in ship-shape forms 
consist of wave making and skin friction. It is evident from the 
remarks made by Mr Mansel that he totally misunderstands the 
work done by Mr Froude in dealing with the skin friction portion 
of the resistance. Mr Mansel takes much trouble to show that there 
were experimenters before Mr Froude, who had arrived at the same 
figures for the skin resistance of full-sized vessels. I welcome any 
corroboration of Mr Fronde's experiments, whether ancient or 
modem. But Mr Mansel goes entirely beyond such a consideration 

when he assumes that Mr Fronde's rates of surface friction are un- 

25 



186 On Progressive Speed Trials. 

reliable, becaase the rate per square foot of surface for a propeller 
blade was more than double of that for the " Greyhound." What 
Mr Froude did discover about the surface friction and what alone 
enabled him correctly to eliminate this element from the comparison 
of ship and model, was that the rate per unit of surface increased at 
the surface decreased in absolute length. Mr Froude further very 
largely defined the amount of such increase of friction with the 
diminution of length. The apparent discrepancy, therefore, between 
the surface friction of the *^ Greyhound " and the surface friction of 
the propeller, instead of being a proof of Mr Fronde's being in error, 
was an indication of his discover}\ But I am afraid Mr Mansel was 
too eager to find Mr Froude in the wrong to accept this hint, and so 
fell into error and mistook a truth for a blunder. 

Mr Mansel objects to model trials on the ground that, "the 
absence of the propeller entirely alters the character of the pheno- 
mena." Would it not have been just to Mr Fronde's memory to 
point out that he, first of all model experimenters, introduced the 
propeller as a means of analysis into such experiments) By doing 
this, he determined the existence of the augmentation of resistance, 
and the relationship between that element and the power recovered 
by the propeller from the wake. 

In my paper I pointed out that in his Letter of Reclamation, Mr 
Mansel had (possibly unintentionally) very much misrepresented Mr 
Froude in his use of the square of the speed. After hearing my paper 
I thought he would have had the generosity, in his reply, to admit 
his error, and to do justice to Mr Froude. But instead of this he 
says in his reply, *^ Dr Froude making use of the same equation I 
published in the spring of 1875, from (8) and (4), deduced the value 
/— 10*04, which is simply the result of an assumed false law of 
resistance masking the mechanical principle involved in Morin's 
constant." From this quotation it would appear that Mr Froude in 
determining the initial friction of the ^'Merkara" had used Mr 
Mansel's formula V^ = C (P + rp — 6). But if we refer to Mr 
Fronde's paper in the spring of 1876, and deduce the formula which 
underlies his graphic determination of the initial friction, we shall 



On Progressive Speed Trials. 187 

get the expression V^-« ' « c (T — /). Here T is equal to the indi- 
cated throst, and / to the amount of initial friction expressed in 
indicated thrust,' the power 1-87 expressing the rate — determined by 
Mr Fronde's experiments— of variation of skin friction with varying 
speed These formulaB on the very face of them are not the same, 
the most marked difference being certainly that between the figure 
5 and the term /. In Mr Mansel's formula the initial friction is 
assumed known, and is put down in figures. In Mr Fronde's 
formula the initial friction is an unknown quantity which has to 
be evaluated by the formula. Herein lies the whole gist of the 
matter. Mr Fronde saw that the initial friction could be discovered 
by reducing the power ordinates to force ordinates — hence his 
formula. Mr Mansel assumed that he knew the initial friction, and 
therefore did not attempt to use his formula for the same pur- 
pose. But even ignoring this there is the further difference that 
while Mr Froude knew clearly the limits of application of his 
formula, Mr Mansel has as clearly shown in his Letter of Reclama- 
tion that he had no conception of these limits. 

There is a sentence quoted by Mr Mansel from Mr Fronde's rider 
to the British Association Report, which calls for some remark. As 
quoted by Mr Mansel, it has been mutilated by the omission of the first 
thirteen words — ^that is, of all the words down to " conclusion that." 
I give the sentence in full : — " Now, Professor Rankine's admirable 
streamlineinvestigations have definitely established the conclusion that 
for symmetrically shaped bodies of ^fair' lines, not excluding by that 
description certain very blunt ended ovals when wholly submerged, 
the entire resistance depends on the conditions of imperfect fluidity, 
of which surface friction is the only one so considerable that we 
need take account of, if we deal with bodies of rational dimensions." 
Mr Mansel goes on to say, that ''The statements quoted are samples 
of a soil suited to the development of 'new departui'es,' which anon 
shall blossom and fructify into 'Popoffkas,' length and breadth 
synonymous, and war ships ' short and handy,' which a Reed not 
shaken by but controlling the winds shall extol magniloquently and 
old Neptune, most misanthropical of <pike-keepefs,'by his unpublished 



188 On Progrt$9m Speed Trials, 

table of rates, shall toll most exorbitantly." Mr Mansel in saying 
^^ statements " refers not only to the submerged body described in 
the previous quotation, but to the strange resdts given by the 
swan-breasted model upon which Mr Froude experimented be- 
fore the formation of his tank. It is unfortunate for Mr Mansel 
that at this present moment facts seem to be against him 
and in favour of Eankine and Froude. I understand that Mr 
Whitehead, in his newest type of torpedoes, is adopting forward 
ends, not of the sharp form which these totally submerged bodies 
originally had, but like those described in the quotation made by 
Mr Mansel — viz., very blunt ended ovals. It is very curious also 
to observe, as I had the pleasure of doing lately in Mr Yarrow's 
yard at Poplar, that the fastest torpedo boats are being built with 
very much blunter forward ends than was the practice some few 
years ago. In cases of this kind, we must depend more upon 
practice and experiment than on what mere abstract theory would 
lead us to expect. It will therefore, perhaps, be well with regard 
to the swan-breasted model results, not to be positive that they too 
may not some day have practical confirmation. 

In conclusion, I would express my regret that the course of this 
discussion has, on Mr ManseFs part, turned from a defence of his 
own work to a depreciation of Mr Fronde's. To you, as to myself, 
it must have been painful to listen to the depreciation of a man 
whose generosity led him so amply to admit his indebtedness to 
your great townsman, Rankine. It was a poor return, before this 
Institution, of which Bankine was so great an ornament^ to have 
heard Fronde's achievements minimised, and the fruits of his genias 
and labour treated as of little value. He was almost the first among 
the scientific men who helped naval architecture, to think it a 
task not unworthy of his powers to make himself understood by 
practical men. There was no contempt in him for his fellow-men 
less skilful in mathematical processes than himself, and he never 
undervalued others because they were only plainly trained. He 
possessed in a remarkable degree ,and combination the gifts of a 
great thinker, a great experimenter, amd an admirable teacher 



On Progressive Speed Trials. 189 

Eyen yet we only know a portion of his work^ for there lie boned in 
the Admiralty archives many of his most valuable reports, and the 
results of very many of his experiments. I trust the day is not far 
distant when^ instead of depreciation, his memory will receive the 
deserved honour of the publication of his completed works. This 
would be the best monument to a memory cherished by every one 
who had the honour and the happiness of his friendship. Without 
the morbid jealousy and vanity which often lead a man to crave for 
priority, and to despise his less accompUshed fellow-men, Mr Froude, 
by his simple, constant, and unbiassed love of truth, passed a life in 
which the endowments of his heart and spirit were as apparent as 
the power of his inteDect. Indeed, to have known him was to have 
had the opportunity of becoming a better man. 

On the motion of the Presidsnt, a vote of thanks was passed to 
Mr Denny for his paper. 



[Appendix.] 

Translation from the 

"Cours de Mecanique/' par F. B^ch^ 

Directeor de I'Ecole d'Application du Qisde Maritime. 

Section V. 



On the Theorem of Newton on Similarity of Motions^ considered as a 
Oeneral Principle for -all Questions in Applied Mechanics. 



1. In geometry two figures are similar when one can be deduced 
from the other by means of a changeless ratio / between the homolo- 
gous sides without change of the angles. 

2. In the statics of rigid bodies, if any system of forces P, P', P', 
acting on any figure, be in equilibrium, then the same forces miUti- 
plied by any number /, will be in equilibrium on the same figure, or 
on any similar figure. 

3. The general theorem of similarity in statics is thus verj 
simple and very broad, because we can arbitrarily fix the two 
co-efficients or ratios /, /. 

However, in terrestrial applications, we are obliged to take int4) 

account the weights of the bodies among the forces P, P', P* 

of a system, and thus there are two cases to be distinguished — the 
one ideal, the other real. 

4. The ideal case is such as would be obtained by imagining bodies 
of finite volumes at great distances apart, their centres of gravity 
being united by rigid straight lines; the co-efficient I would then 
only have reference to the figure of the rigid lines, and the co-efficient 

/ only to the weights 11, 11', 11" of the different bodies, so that 

there would always be a complete independence between the co- 
efficients Ijf, so long as the volumes of the different bodies did not 
exceed the limits beyond which these volumes would penetrate one 
another. 

5. The real case is that in which there is only one ratio of 



I 
I 

On Progressive Speed Triak, 191 I 

similarity / in all parts of the system ; denoting then by d the ratio 
of the densities or the specific gravities we necessarily have 

because the weights of similar bodies follow exactly this law^ and 
all the other forces P, P', P', most in consequence do the same. 

6. In the statics of flexible bodies the equations of equilibrium 
are 

= X + 2E f ' 
dx 

dr 

= Y + 2R ^"^ 

dy 

fur all points z, y, z, of a system, and the functions 

can certainly be such that, in two exactly similar positions, before 
and after the deformation of the system, the forces X, Y, Z, which 
produce this deformation, will not vary in a single and identical 
ratio /. 

BBiThence, inversely, when the forces X, Y, Z vary in one same ratio 
/, the subsequent figure of the system can be not similar to the initial 
figure. In fact, if we imagine a prismatic bar laid horizontally on 
two supports, under a vertical load in the middle, we may see that 
the deflection of this bar increases directly as the load, without 
increase of the chord of the arc, which will evidently hinder the 
new figure of equilibrium from being similar to the previous one. 

Likewise, a prismatic bar drawn out in the direction of its length 
only, would be lengthened without becoming thicker, &C., &c. 

Thus we cannot pretend to extend the theory of similarity in 
statics to cover small changes of figure which a body under the 
infiuence of diiSerent forces will undergo. 

We can, indeed, propose to establish a comparison between two 
bodies of large and small dimensions, supposed similar in their initial 
forms when there are no forces X, Y, Z at play, and similar still 
in their subsequent forms when the one is acted upon by forces 



193 On Progre$$ive S^eed Trials. 

X, Y, Z, and the other by corresponding forces X', Y', Z' ; because, 

applying the ordinary formole in the theory of the resistance of 

materials, we leam that in this case, for the same kind of materiil 

and with the same quality of elasticity, there exists for the two 

bodies only the single ratio 

/» 

between the absolute forces which must be applied on the one bodj 

and on the other to homologous surfaces. 

It follows that the theory of similarity in statics can be eiztended 

thus when we make 

/=/Sor/=l, 

according as we denote by the letter / the ratio of the resultant 

forces on two homologous and similar surfaces, or else the ratk 

of the resultant forces per unit of surface at two homologous points. 

but we cannot submit to the same law the forces of gravity, tbc 

ratio of which, from the one body to the other, and for the ssine 

density, is 

/». 

Moreover, the forms of two bodies similar and similarly bent^ d 
large and small dimensions, are not equally resisting forms, and iff 
these reasons we can only extend the theory of similarity to the sta& 
of flexible bodies by neglecting such small changes in the figure i^ 
the bodies undergo under the action of the force that is applied 
which evidently amounts to considering only entirely determiofii 
and previously known figures as in the statics of rigid bodies, is 
which case the theory in question is reduced to what has alreiij 
been stated. 

7. To extend the same theory to dynamics, it is sufficient to ' 
note that the total exterior forces acting on a moving body c^ ' 
be represented by the quantities 

Xl = X-m^ I 



On Progressive Speed Trials, 193 

aud th&t, consequently, the complex quantities X, Y, Z ought to 
increase all in a single and identical ratio /, when we pass from any 
system to another exactly similar. 

8. But in considering the co-ordinates x, tj, z o{ & material point 
of mass 771 as functions of the arc s of the described curve, and the 
arc 5 as a function of the time, we have 

dx dx dj ^dx 

di^ ds dt' d4i^' 

foi'ther, by considering also the velocity t' as a function of the are s, 

we find 

d^x dx dv ds d^ ds ^ vdv dx ^d^ 
W^dsdsdt'^ds^di^^ ds ds ^ ^ ds^' 
so that, denoting by 

a ,3, y the angles that the velocity v makes with the rectangular 

axes of Xj y^ z^ 
r the radius of curvature of the path considered as essentially 

positive, 
a, h, c the angles that the radius r drawn from the circumference 
towards the centre, makes with the axes of x, y, z, 
we have 

d^x vdv , o" 

rf/^=="3?^'" +--cosa 

d^y vdv o.v^ J 

T*'> = -J COS p + - COS 

at'' as '^ r 

d^z vdv , V' 

_.= _ cosy +- cose 

9. It follows from this that from one* system to another, the 

quantities 

dH d^ d^ 
di^ ' df^ ' dl^ 

can vary in many different ways ; but when we wish only to make 

comparison between the homologous points of two similar systems, 

and when we wish at the same time to have similar paths, in order 

that the similarity of the two systems may hold indefinitely, then 

the angles «, j3, y and a, b, c must be exactly the same two for 

26 



1 94 On Progressive Speed I'riak 

homologous points, and the dynamic forces in questbn must vmrj 
partly as the term 



and partly as the term 

vdp 

Si' 

10. Thus, denoting by u the ratio of the velocities of two homolo- 
gous points, and keeping the letter / to denote the ratio of the 
linear dimensions, we shall have, in the other system, the velocity 

and the corresponding forces, 











/ r 


v'dv' 
d$' 


S 


m (vdv + 


vdu) 


(•; 


+'. 



by which we see that from the first system to the second the ratio 
of the centripetal forces will be 

and the ratio of the tangential forces 

tt* vudu 

f^ldv' 

Then the ratios of these two kinds of forces cannot be the same 

unless we have 

v' 

- = ttas Const (1) 

and when this condition is accomplished, the common ratio of the 
quantities 

d^x d^y d*z 

di^' di^* dt^' 
between two homologous points of two exactly similar systenis, 
becomes the perfectly determined number 

T 
that is, the quotient of the square of the ratio of the velocities 
divided by the ratio of the linear dimensions. 



On Pro^rtssm Spied Trials 195 

11. As the ratio of the homologons masses in two similar systems 
is 

m ' 

where the letter d denotes the ratio of the densities, we see that the 
ratio of the forces of inertia 

dhi d^ d^z 



«• 



wfllbe 

/« (^/» X J = lift** (2) 

and consequently all other forces, the components of which have been 
denoted by X, Y, Z, will need to vary in the above ratio : that is to 
say, as the density, as the square of the linear dimensions, and as 
the square of the velocities. 

12. The ratio of the durations ijt oi two homologous movements 
wiUbe ^ t I 

and this would be Uie whole theorem of similarity in dynamics, if 
we could n^lect the forces of gravity. 

13. It follows from this that in the absence of the forces of 
gravity, the resistances of floating bodies of similar forms and of 
absolutely smooth or polished sides would vary exactly as the densi- 
ties of the liquids, as the homologous surfaces, and as the square 
of the speeds, provided that the atmospheric pressure per unit of 
area at the free surface of these liquids were to vary also according 
to the same law, and would consequently be proportional to the 
density as well as to the square of the velocity. 

14. But in terrestrial applications we cannot generally neglect the 
forces of gravity, and then all the other forces must vary as these, 
that is to say, to the general relation 

we must link the condition 

^• = ^ (8) 

which involves that 

f^dl^ 
or the other forces as well as for the forces of gravity. 



196 On ProgresHoe Speed Irials. 

15. The condition 

«« = / 

is more necessary when the forces of gravity predominate over the 
others in a system : that is to say, when the motion is relatively 
slow; it is less necessary, on the contrary, when the forces of 
gravity mg are small in comparison to the forces of inertia, 

cPx d^ dz 

""^di*' -"^d?" -^"^df 

or when the motion is relatively rapid. 

16. It follows from this that the resistance of a floating body at 
different speeds, and with a suitable pressure at the free surface of 
the liquid, must approach indefinitely towards proportionality to the 
square of the speed, as the motion grows more rapid, and must 
depart^ on the contxary, from such proportionality as the motion 
grows slower. 

17. The exact proportionality to the surfaces and to the square 
of the speeds cannot hold good, in a word, unless we operate on 
similar forms^ and with the condition, 

Thus, in the case where we have determined experimentally, by 
means of certain known forces, the resistance of a ship's model, or 
rather the complete behaviour of a model of a paddle or screw 
steamer, we have only to make another model with linear dimen- 
sions / times larger, and to multiply all the observed speeds by the 
ratio _ 

that the new system may behave similarly to the previous one, 

requiring forces, the statical intensities of which are all increased in 

the proportion of the cube of the ratio of the linear dimensions, 

which increases the quantity of work of each of these forces as the 

product 

dlH = dl^u^. 

18. Or conversely, in the case where the dimensions and speed of 
a ship or steamer are known, and we propose to experiment upon a 



On Frogremve Speed Trials, 1 97 

small model so as to find all the relations of the forces and the speeds 
of the system, we have to use the same formula, 

in order to find the precise ratio of the speeds which we must 
establish between two homologous points of the two systems, so that 
the ratio 

can serve for passing exactly from each of the forces of the large 
system to the corresponding force of the small model, or vice vena. 

19. However, for perfect similarity, the atmospheric pressure at 
the free surface of the liquid, as well as the frictional forces or the 
forces of adhesion of the liquid particles against the sides of the 
system should follow the same general law as the other forces : that 
is to say, should be proportional to the cube of the ratio of the linear 
dimensions on two homologous surfaces, and consequently propor- 
tional to the ratio of the linear dimensions, or to the ratio of the 
square of the speeds, per unit of surface. 

20. But it is very probable that for nearly incompressible liquids 
such a restrictive condition for the atmospheric pressure is not 
necessary unless the extreme rapidity of the motion of a body 
wholly immersed produces at the after end of the body a wake 
completely empty, or at least full of vapour, such as exists, perhaps, 
at the after end of a cannon ball, which moves at a speed of 400 to 
500 metres per second in a sufficiently dense medium. 

21. As to the adhesion or the friction of a liquid against a con- 
tinuous surface, the very little we know up to the present day seems 
to indicate that the forces of this kind vary, in fact, about as the 
square of the speed. 

22. What we have now said shows sufficiently that in mechanics 
the theorem of Newton on similarity is always the best, and often 
the only principle on which we can base numerous practical 
deductions. 

23. This single theorem include? about all that men have managed 
to establish in hydrodynamics up to the present day by more or 



198 On Progressive Speed Trials. 

less empirical or defective means, and when we add to it the tbeor; 
of the vis viva by M, Coriolis, as well as our theorem on the forces 
of reaction, we shall possess a science more simple and much more 
powerful than any we could derive, up to the present time, from the 
special formulae in hydrodynamics, the utility of which seama to be 
absolutely m/ in a course of terrestrial mechanics. 



NoU an Tetis of TuriMW, by Professor R, H. Thubston 



Beeemd 10th November, 1884 



I note a few points which were brought up, in the course of debate 
upon the note sent to the Secretary, by me, last spring, which 
demand reply. 

Mr Tombull suggests that the tests referred to by me were made 
some months after those reported by him, and that there may have 
been some improvement in the interval. I would say that the 
builders of the wheel described are constantly experimenting with 
their turbines, testing them at the flume, and making alterations 
and improvements suggested by the results of such tests, and are 
thus constantly improving it. It is their avowed intention to thus 
improve all of their wheels until every pattern put on the market 
shall have an efficiency, under, say, 20 feet head, of above 80 per 
cent. 

Ifr Murray expresses doubts in regard to the figures reported by 
me, and asserts that I have given nothing they could well found 
upon, to improve their knowledge in this matter. He goes on to 
XK>int out an apparent discrepancy between the data given, as 
evidence that I have been careless in reporting, or that the tests 
are not reliable. The apparent discrepancy is accounted for in the 
simplest way imaginable : the heads under which the wheel worked 
at full gate, on the two dates mentioned, were slightly different, in 
consequence of the variation of flow in the Connecticut River, and 
of rate of demand for water on the part of the adjacent mills. I 
did not consider it necessary to encumber the Transactions with 
extended tables of details, and gave simply results. If desired, I 
will gladly give the full logs of those tests, and of just as many 
more as may be needed to show that my statements may be abso- 



200 Oti Teds of Turbhus. 

lutely relied upon. The probable error of the trials at the iiiime of 
the Holyoke Water Power Company is, I think, not more than one 
per cent. Any other apparent error that any critic may discover in 
the data famished will be found, I doubt not, to have eqnallj 
simple explanation. The fact is that these turbines did do exactly 
what has been claimed for them. I have superintended their tests, 
examined and measured up the flume, gone over the system of 
working up results, and may claim full credence for every assertion 
which I made in my original contribution. We are not unaccus- 
tomed, in the United States, to seeing 80 per cent, reached. We 
have many wheels that have given that figure, under favourable 
conditions ; and the wheel in question is always expected to exceed 
that figure after the makers have worked their patterns into such 
a shape as satisfies them. But we are not alone in this matter. 
The turbines of M, Vallet, the distinguished French hydraulic 
engineer, have repeatedly given efficiencies exceeding 80 per cent., 
and I have no doubt that other good designers of turbines reach 
that figure. We do not consider it by any means wonderful, even 
for turbines with cast iron buckets. I have records of a number of 
wheels tested, under such conditions and by such skilled hands as 
to make it certain to my mind that the figures are correct, which go 
above 80 per cent 

I agree fully with Professor Thomson in his impressions in regard 
to the probable success of the untaught mechanic attempting to 
solve the problem here considered, and the fact of success in this 
case was to me, as to him, a very interesting and an almost 
incredible one. Nevertheless it remains a fact — a fact of which I 
am personally thoroughly certain. The man has produced turbines 
having efficiencies reaching up to 85 per cent. He cannot do this 
at every attempt^ and, as might be expected, cannot with certainty 
repeat a success. Working with an educated and skilful engineer, 
I have no doubt that his successes would be more frequent and his 
work more uniform in quality. 

HoBOKEN, N.J., U.S.A., Oct., 1884. 



On Ekdncal Navlgaiion. 
Bv Mr Allan Clark. 



(SEE PLATE XVll*.) 



Received 16th December, 188iy and held as read 24ih February, 18So. 



In treating this subject, we shall confine it to a short description of 
what has already been accomplished, and which may be found inter- 
esting, as showing the improvements which have been made up to 
date. Firstly, in regai'd to the batteries that furnish the current of 
electricity, and secondly, in regard to the motors which turn that 
current into mechanical work. 

We shall, for the sake of compaiison, given details of the spaces 
occupied, and the weights of the various batteries and motors, to- 
gether with the horse- power furnished by the batteries, and the jier- 
centage of efficiency of the motors. 

The batteries are either primary or secondary. The primary battery 

may be regarded as a kind of furnace where the fuel is zinc, the 

cuiTent of electricity being derived from the potential energy of 

zinc in the process of its dissolution and combination with oxygen 

to form oxide of zinc. Considered thus^ the voltaic furnace can be 

shown to be a much more perfect and economical arrangement 

than the steam furnace, in which all heat of a low grade is wasted 

or lost. In the electric generator all potentiality is utilized. The 

secondary battery or accumulator may be regarded as a cistern for 

storing the current of electricity derived from a dynamo or primary 

battery. This current once stored, may be drawn off slowly or 

quickly as desired. 

The motor that converts the current of electricity into mechani- 

27 



202 On Eiedrical Navigation, 

cal power is an arrangement of soft iron in two parts, one fixed and 
the other movable, usually in the form of a drum revolving inside i 
frame. The current passes through an insulated copper wire wound 
round these — in the fixed frame in one direction only; but in tk 
movable part the current is reversed at certain points whereby' a 
continuous magnetic attraction and repulsion is kept up between 
them causing the drum to revolve. 

The first experimenter in electrical navigation was Professor 
Jacobi, a Russian, who in 1838 succeeded in propelling a boat 27 
feet in length, on the river Neva, at the i^te of one and a quarter 
knots per hour. The battery used consisted of three hundred anil 
twenty Daniell cells, occupying a space of sixty cubic feet, and the 
motor a space of ten cubic feet The battery furnished a current of 
one horse power, and the motor had an efficiency of ten per cent. 
The boat was wrought through the medium of paddle wheels. A 
sketch of this motor may be found interestiug, especially as it W3^ 
one of the first known to history. 

An experiment similar to that of Jacobi was exhibited by Mr 
Llewelyn to the members of the British Association at Swansea in 
the year 1848. The motor used on this occasion was a grea: 
improvement on those previously invented, but the battery was too 
wasteful of zinc for practical purposes. 

In 1866 Count de Moliu succeeded in constructing a motor, th^t 
drove a small boat in the Bois de Boulogne. His motor developeii 
one-seventh of a horse-power at the cost per hour of thirty-eighi 
pounds of zinc per horse-power. 

In 1881 Mr Gustavo Trouve, of Paris, constructed a twenty-foo: 
boat that was worked in the little lake at the Exhibition. For tlib 
he made use of small double motors of the simple Siemen's armature 
kind, fixed on the rudder head, and connected to the propeller by 
means of an endless chain. The battery measured four cubic feet, 
developed two-thirds of a horse-power, and the motor an efficiency 
of nearly twenty per cent. A speed of between two and three miles 
per hour was obtained. 

Late in 1882 the Electrical Power Storage Company, of LondoD. 



On Electrical Navigoiioii, 203 

produced the launch " Electricity/' a boat twenty-five feet long, and 
which differed from any of the preceding in having accumulators 
instead of primary batteries to furnish the driving power. Forty- 
five accumulators were used, each weighing half-a-hundred weight, or 
twenty-two and a-half hundredweights together, and the space 
occupied was fifteen cubic feet. The motors used were two Siemen's 
dynamos, weighing six hundredweights, and occupying a space of 
seven and a-half cubic feet. These were connected by belting to an 
overhead shaft, which in turn was connected to the propeller shaft. 
For reversing, this belting was shunted to a loose pulley, and a 
crossed belt connected up — an arrangement primitive and bulky. 
The total weight of accumulators, motors, gearing, and huU, was 
upwards of two tons. The accumulators furnished four-horse power, 
and as the motors had an efficiency of about seventy per cent., 
nearly three horse-power was obtained, and a speed of between five 
and six miles per hour. 

Early in 1883 the author, who had been experimenting for some 
time, produced his first full-sized launch, which was twenty-one feet 
long. The batteries occupied a space of three cubic feet, and the 
motor a space of about half-a-cubic foot, and weighed together two 
and three-quarter hundredweights. The total weight of this launch 
was four and a-half hundredweights. The battery gave off one and 
three-quarters horse-power, and as the motor developed fully one 
and a«quarter horse-power, its efficiency was about seventy-five per 
cent. The propeller was a two-bladed one, twelve inches diameter 
and thirteen inches pitch, giving four hundred and fourteen revolu- 
tions, and a speed of four and a-half miles per hour. The reversing 
and stopping gear used was a simple cut off and current reversing 
bobbin, which weighed a few ounces only. This was the first 
electrically-driven boat that had the propeller shaft coupled directly 
to the motor, and marked a very important advance. 

In obtaining this result several difficulties were overcome. The 
style of machinery that had given satisfactory results in the model 
was found to be useless owing to the lower rate of revolutions 
required. Electrically driven motors work best when allowed to 



204 On Eledrical NarigaHon, 

revolve fifteen hundred to two thousand revolutions per minute, with 
a light load ; but when loaded to revolve only four hundred per 
minute, the copper wire gets heated and the insulation destroyed, 
rendering the motor useless till re- wound with fresh wire. By in- 
creasing the size of the motor it was found that with the same 
current the large motor gave better results than the smaller one, and 
the wires did not heat. The bilge water was found also to damage 
the insulation of the copper wire, allowing the current to pass with- 
out going its round through the wires. By water-proofing the motor 
all over, this difiiculty was got rid of ; also several minor ones. 

For comparison with the accumulator launch '< Electricity " details 
of the author's launch " Electric," also 25 feet long, are now given. 
This boat was officially tried in May last. The battery occupied a 
space of six cubic feet, and the motor fully a cubic foot^ weighing 
respectively three and one and a-half hundredweights; the total 
weight of hull complete with machinery was seven hundredweights. 
The battery gave off three and a-half horse-power, and the motor 
nearly three horse-power. The propeller was two-bladed, fifteen 
inches diameter, and eighteen inches pitch, giving three hundred and 
ninety-six revolutions per minute, and a speed of five and seven- 
eighth miles per hour. 

In one of the same size now finishing the battery is four horse- 
power, and with a more efficient motor it is expected a speed of 
seven miles per hour will be got, which is about the maximum that 
can be got from a boat this size whether the power be electricity or 
steam. 

It will thus be seen that the batteries have been improved from 
sixty cubic feet per horsepower to under two cubic feet per horse- 
power, and the motors from 10 cubic feet for one-tenth horse-power 
to about one cubic foot for three horse-power or about three thousand 
per cent, on each. The consumption of zinc has also decreased from 
thirty-eight pounds in 1866 to one and one-third pounds per horse 
power in 1884. 

As to the future of these vessels, it is not expected by the most 
sanguine that they will ever supersede steam even on a small scale, 



On EUcWical Navigation. 205 

bat they will certainly obtain a footing for pleasure purposes where 
the utter absence of noise, smell, and soot is an advantage that users 
are willing to pay for, even were the cost much more than it is now. 
Among the many advantages these boats driven by primary batteries 
exhibit over steamers may be mentioned. They can be charged in 
one-third the time it takes to get up steam. When charged they 
can be used at once or weeks after without further trouble. After 
being used, they can be left without attendance, and used again 
when required* They do not weigh more than one-third the weight 
of steam launches the same size, can be easier hung on davits, are 
cleaner and noiseless, and do not require skilled attendance. 

The accumulator launches require motive power to drive a 
dynamo to charge the accumulators, so that it is not likely these 
boats will come into use except perhaps for ferry or coast traffic, 
where the charging plant could be kept at the terminus quay and 
applied as required. 

Regarding cost of driving, if steam be taken to represent 1, then 
accumulators may be taken at 2, and primary batteries at 10; but 
as improvements in primary batteries are being made continually, 
it is probable this figure will be much reduced ere long. 

On the 24th March, 1885, the President, in proposing a vote of 
thanks to Mr Clark for his paper, said he had no doubt that the 
Institution were gratified by having the information contained in the 
paper put on record. Electrical propulsion was a very interesting 
subject, and while he did not think it would to any great extent 
supplant lihe use of steam in navigation, yet it might have its own 
uses ; and it was highly desirable for them always to be on tlie 
outlook to find what were the capabilities and uses of electricity in 
various directions. 



On a Continuous Regenerative Qas Kiln for Burning Fir$-hricksy 
Pottery^ &c. 

By Mr John Mayer, F.C.S. 



(see plate XVIII.) 



Received and Read 24th March^ 1885. 



For fully twenty years the subject of firing by using fuel in the 
gaseous form, and on the principle of heat-regeneration, has had a 
most intense attraction for me, partly on account of the scientific 
interest and beauty inherent in it, partly owing to its great import- 
ance in the industrial arts, and in no mean degree in consequence of 
its being made the theme of the last public discourse delivered in 
the Boyal Institution, London, by the late Professor Faraday, which 
was the only occasion on which I had the great pleasure of listening 
to that distinguished chemist and physicist, and of seeing him 
perform many beautiful experiments with matchless skill and success. 
That was in the year 1862, while the Great International Exhibition 
of that year was being held in London ; and on that occasion the 
great experimental philosopher was surrounded by many of the most 
notable scientific men of this kingdom, of the Continent of Europe, 
and of the United States of America. The late Sir Wm. Siemens, 
who was then rapidly making his great reputation in physical and 
mechanical science, had quite recently got his regenerative system 
of gas-firing into successful operation at the famous glass works of 
Messrs Chance Brothers, at Birmingham ; and so greatly charmed 
was Faraday with the beauty of SiemensV valuable invention that he 
made a special journey to the capital of the Midlands in order that 
he might look into the glass-melting furnace with his own eyes^ and 



208 On a Continuous 

thereby be enabled to appreciate the merite of the invention in their 
true and full significance. It was upon that subject that ^' the old 
man eloquent " delivered his most memorable discourse, and during 
all the many years that have since elapsed the Siemens system of 
gas-firing and heat-regeneration has never in the least d^ree 
diminished in its scientific beauty and value, while as regards its 
importance in the industrial arts it has gone on from year to year 
attaining for itself a stronger and stronger position ; indeed, so veiy 
marked is that the case that the system in question may be spoken 
of as one of the greatest industrial inventions of the present geners 
tion. 

Within those years there have been many and varied applications 
of gaseous firing and heat-regeneration, according both to the 
Siemens patents and to the patents of other. inventors. It is the 
aim of this paper to describe another successful application of those 
two principles, alinost at our own doors, as it were, and in a branch 
of manufacturing industry in which there was great room for 
economising fuel and preventing the fouling of the atmosphere bj 
the discharge of immense volumes of dense black smoke. The 
industry to which I refer is more especially the burning of fiire-bricks, 
though it may also be said to iuclude all kind of goods that are 
made of clay ; and the inventor of the system of kiln-burning about 
to be described is Mr James Dunuachie, who has been intimately 
identified with the manufacture of that most refractory and heat- 
resisting, and now and most familiar article — a '^Glenboig fire 
brick " — for the last quarter of a century. Various persons, includ- 
ing Dr Siemens, had made attempts to produce a kiln for firing 
bricks on the heat-regenerative principle, but in no case were anj 
efforts in that direction attended with practical and commercially- 
successful results until the matter was taken in hand by the 
proprietor of the Glenboig Star Fire-clay Works, some four or five 
years since. 

One important factor for making kiln-firing by regeneration t 
success was a means of providing a continuous supply of gaseous fuel, 
in a cheap and easy manner, and at that time such an appliance was 



Regenerative Gas Kiln. M9 

ready to hand in the gas-producer which was brought under the 
notice of the members of this Institution some time ago by 
Mr F. J, Eowan. Without in any way detailing its construction 
or mode of action, I may pass on and simply state that such 
a gas generator, similarly to that of Siemens, produces gaseous 
fuel whose combustible constituents usually form well-nigh 40 per 
cent, of the whole, the non-combustible diluent being chiefly 
atmospheric nitrogen; and it may be well here to state that the 
chief combustible and calorific ingredient of producer gas is carbonic 
oidde. As r^ards the kind of fuel to be employed in the proposed 
new mode of burning fire-bricks, Mr Dunnachie had long had his 
mind made up, his desire on this point being to follow in the foot- 
steps of Siemens ; and as to the mode of practically using the gaseous 
fuel to the greatest advantage he also had his mind made up. Of 
course, it inyolved the adoption of the principle of heat-regeneration, 
and in a way not only modified to suit the special circumstances of 
the case, but so radically differing from the Siemens system of 
regeneration that the device adopted practically amounted to a new 
and important invention. 

Two producers were forthwith ordered, and in due course erected 
on a suitable spot within the works ; and at the same time, Mr 
Dunnachie proceeded t-o erect a kiln embodying all the newest 
notions that seemed to accord with the most efficient method of 
developing the calorific powers contained in the gaseous fuel. 

Fully three years ago the first continuous regenerative gas kiln, as 
it was evolved from the brain of the inventor, was brought into full 
work, and it at once established itelf as a very marked practical 
success. Since that time the system has been extended at the 
'* Star " Works, and it has also been brought into use at the original 
Glenboig Works, and at the Cumbernauld Fire-clay Works — ^all the 
three establishments just named being now the property of one 
concern, the Olenboig Union Fire-clay Company (Limited). Of its 
applications elsewhere and of its prospective adoption in other 
directions something may be said further on. 

As illustrated by the diagrams exhibited on the walls, and by the 



210 On a Continuous 

very excellent and instructive model placed on the table (the latter 
having been put at my service for this evening, prior to being sent 
to the International Exhibition of Inventions about to be held is 
London), it will be seen that the continuous regenerative gas-kih 
under consideration is really a series — or, better still, two series— 
of separate kilns or firing-chambers which are well seen in tlw 
ground plan (Fig. 1, Plate XYIII.) That plan, taken along with 
Figs. 2, 8, 4 (Plate XYIII.), shows that there are two parallel masses 
of brick-work about 24 feet apart, each of which contains five separate 
firing-chambers, which are all connected with each other in a series, 
by means of flues situated underneath the floors and in the walls of 
the individual chambers. These flues are for conveying the gaseous 
fuel from the gas-producer and the air which Ib to be used in its 
combustion wherever it is required. Situated opposite the middle 
of the 24-feet open space, and at a short distance outside, there are 
seen represented the two gas-producers with their overhead effluent 
tubes, and the latter are seen to terminate in a series of underground 
flues, which again terminate in the individual firing-chambers. 
There are likewise shown on Fig. 1, Plate XVIII., a number of other 
flues which terminate in two common undei^ound passages bj 
means of which the waste gases, after having done their regenerating 
work in the way of yielding up their surplus heat to the incoming 
air, pass into the chimney stack. It may here be mentioned that the 
stalk at the '* Star " Works, and which is shown in the model, and 
its position indicated in the ground plan, is about 120 feet in height 
which (in addition to doing other work) is quite sufficient to produce 
a good draught. If a blower be used for the air, the chinmey maj 
be dispensed with, or one not so high may be employed. StiD 
referring to Fig. 1, Plate XVIII., it may be observed that right over 
each individual gas flue leading to its respective firing-chamber, there 
is placed a valve for controlling and regulating the amount of gas 
passing into any chamber. Then, again, there are provided dampers 
for keeping the currents of entering air and effluent waste gas under 
the most perfect control. To an observer who sees this kiln in 
operation for the first time and can appreciate its merits, it would 



Begeneratm Cfas Kiln. 211 

almost seem as if the ultimate effect of all the nicely hannonised 
arrangements were even more beautiful and scientifically perfect 
than the original conception of the inventor could have been. 

It is perhaps scarcely necessary to give a detailed series of dimen- 
sions bearing upon the construction of one of these regenerative gas* 
kilnS) but a few such data may be mentioned. The extreme length 
of each mass of brickwork containing five firing-chambers is 69 
feet; the length, height, and width of the chambers internally are, 
respectively, 17 feet, 11} feet, and 10} feet; and the internal 
capacity of each chamber is equal to about 13,000 or 14,000 bricks — 
the number varying according to their size and shape. Such experi- 
ence as has now been gained at Glenboig shows that it is possible 
by means of a set of ten chambers arranged according to the plans 
in the diagrams to fire 800,000 bricks per month. By reference to 
Kg. 2, Plate XVIII., which shows the end elevation of one complete 
kiln, or set of ten firing-chambers, it will be seen that the open 
24-feet space, is covered in by means of a light iron roof, so that it 
is possible to carry on all the operations of charging and drawing, 
"steaming" and heating-up, regenerating, firing, and cooling-down, &c., 
in any kind of weather. It may also be noticed that over the space 
just referred to and over the two series of firing- chambers there is a 
floor, formed partly of wood and partly of iron, which is used as a 
drying stove, and on which the moulders pursue their business of 
brick-making so long as there is any room for doing so. This floor 
is admirably suited for drying purposes, as most of the waste 
heat that escapes from the kilns by radiation into the air is here 
utilised in this way. 

A brief account of the way in which these firing chambers are 
employed in continuous series may now be given. Let us assume 
that two of the chambers have been burned off, say, Nos. 1 & 2 
on the ground plan. The current of gas from the gas-producers, at 
a temperature of from 600 degrees to 800 degrees Fahrenheit, is 
turned on to No. 3 chamber, which, up to the present, may be re- 
garded as being a ^^green kiln,*' one in which no distinct combustion 
of gas has yet taken place. The stream of air necessary for the 



212 Onadmiinuoui 

burning of the current of gas, now directed into No. S chamber, is 
made to pass through the mass of finished brick in what we may 
call the bumed-off kilns. Such kilns are the very best regenerators 
that it is possible to conceive of, one of extraordinary efficiency, 
and a '^ green kiln/' properly so called, is the most natural recipient 
and store-room of what would, under other circumstances, be 
waste heat, fiut the term *^ waste heat " in connection with the 
Glenboig regenerative gas kiln is almost, if not quite, a misnomer, 
as there is practically no heat allowed to escape into the atmosphere 
without doing its allotted work, such as regenerating and '^steaming" 
within the kilns, drying green bricks above them, or producing an 
ascensionsd current in the chimney stack. It may be taken as a 
sort of fixed rule in the working of these kilns that the working 
chamber— that is to say, the one on ''full fire" — always has 
one or two, and sometimes even as many as three, burned off 
chambers in its rear in the series and a '^ green" chamber on 
the other side. In its passage through the regenerator the 
stream of air is soon raised to a brilliant steel melting heat^ and 
that is by-and'by imparted to the mass of bricks in the chamber 
which is now passing through the stage of " full firing " — an opera- 
tion that is accomplished in from 24 to 86 hours. But while the 
last-named operation is in progress the next chamber in the series, 
No. 4, is in its turn made the recipient of the heat which is carried 
over by the effluent gases from the chambers where the producer gas 
is actually undergoing combustion ; and in this way its contained 
bricks may become not only dried to perfection, but even heated up 
to redness, which is more or less bright on the side next to No. 3 
chamber, though of a duU red on the opposite side. When bricks 
are stacked in any of these firing chambers, even though apparently 
dry, they always contain a certain amount of moisture which has to 
be driven off in the stage called " steaming " prior to that of full 
firing. In the ordinary course of things, the next chamber in the 
series. No. 5, is at this time the ^* steaming " chamber, and that 
operation may be effected by passing hot air into it from, say, No. 4 
chamber, or it may be done by means of a jet of gas direct from the 



RegenmUive Gas Kiln. 213 

producer, so as thereby not to interfere with the kilns or chambers 
that are on full fire. The vapour as it is dispelled from the green 
bricks makes its escape by means of a number of openings in the 
roof, one of which is indicated at E in Fig. 3. These openings are 
only used when a chamber is undergoing '^ steaming" or being 
cooled down for drawing 3 when full firing or regeneration is in pro- 
gress they are made as close as possible. 

Hitherto I have omitted to state how the gas and air find admis- 
sion into and egress from the individual firing chambers, ten in all, 
and in two series of five each. The gas valves indicated on the 
ground plan, and in vertical section in Fig. 2, can be used at plea- 
sure to admit gas to any chamber by means of the underground 
flues, shown by dotted lines in Figs. 1 and 2, and in section at A. in 
Fig. 8. By means of the same valves the admission of gas may be 
entirely cut off, or the amount of the current may be adjusted with 
the greatest nicety to meet the circumstances of the case. The gas 
passes from the flue into the burner, marked B in Fig. 4, and it 
ascends into the chamber by a series of openings immediately in 
front of the dividing wall of brickwork. What has just been called 
the *' burner " is really a space of about 18 inches that is left be- 
tween the partition wall and the mass of bricks to be fired when the 
latter are being charged. It extends all the way from side to side 
of the firing chamber. The'air required for the combustion of the 
gas, and which is brought in a highly heated condition from the re- 
generator, passes through the floor of the kiln immediately on the 
other side of the partition wall, by means of a series of slits in the 
brickwork, into another flue, shown at F in the same Fig. Along 
this part of the dividing wall there are numerous small apertures 
for the exit of the air from the flue into the firing chambers. The 
hot air and gas meet in numerous streams at or near the floor level 
of the chamber, the resultant effect being most thorough combustion, 
followed by intense heat which is eventually raised to that required 
in steel-melting. Great sheets of flame pass upwards through the 
space above the so called burner, and which space may fittingly be 
termed a heat-radiating chamber or space— much of the value of the 



214 On a Continuous 

Qlenboig kiln being doabUees due to the great amount of radi- 
ation which proceeds from the wall forming the permanent portion 
of the burning chamber. Then, again, the arched crown of the kilo 
also forms a most valuable heat-radiating surface. And here it maj 
be well to mention that the space between the arched roof of the 
kiln and the mass of bricks being fired goes on increasing up to the 
stage of full firing, owing to the shrinkage or contraction in the 
bricks to the extent of about one-twelfth of their bulk. With the 
formation of such a large space above the mass of bricks, the radiant 
heat has an opportunity of exerting its full measure of effect. The 
flames and highly-heated gases in their upward passage swirl oTer 
the top and through amongst the bricks, the effluent or so-called 
waste gases eventually finding their way to the floor of the chamber 
on the opposite or exit side, where there are numerous slits through 
which the gases pass down into the flue marked C in Fig. 4, and from 
which they may proceed either into the next chamber of the series 
or direct to the chimney, as may be desired* By means of the 
gas valves already spoken of, and movable dampers working in the 
flues marked F, the gas and air to be admitted into any chamber 
are under the most perfect control, as they may be decreased or 
diminished in quantity at will, and may be so proportioned as to 
give any quality of flame required. At D, in Fig. 4, there is 
shown another flue about half-way up in the dividing wall. This 
may be used to draw air from one chamber to another at a higher 
level, thus effectually exhausting the heat of the bumed-off kiln and, 
at the same time, shifting the intensity of the heat nearer to the 
back part of the burning kiln or chamber. When it is required, 
the same flue (D) may also be used to admit cold air (by a simple 
arrangement of dampers) in sufiicient quantity to mellow or tone 
down the intense heat of the front, and permit of the back part of 
the kiln being hard burned without injuring the front bricks. 

Up to the present, the description of the mode of working the 
Olenboig gas kibi has scarcely dealt with more than one series of 
chambers, forming half of the complete kiln, fiut those of the other 
series may be regarded as having been in the various stages of 



RegeTieraUve Gas KUn. 215 

cooling-down, drawing, re-filling, &c. As will be seen by again 
referring to Fig. 1, Plate XYIII., there are underground passages or 
fines which give communication between the respective end chambers 
— No. 5 with No. 6, and No. 10 with No. 1. In this way the two 
sets of chambers are made quite continuous, so that practically there 
is a circle in which neither terminal nor commencing chamber 
occurs. 

In devising and working out his gas kiln to be a practical success, 
Mr Dunnachie freely admits that ho has followed the lines of 
Siemens and Hoffman, neither of whom was successful in producing 
a kiln that should be fired with gas, worked on the heat-regenerative 
principle, and be continuous in its action. The former tried his 
hand most anxiously in the direction indicated, but he failed in his 
efforts, and departed from the idea, under the belief that it could 
not be realised. His kiln had not the means of keeping up the heat 
of the regenerator chamber to the high point necessary for com- 
pleting the full-firing operation. A nice white heat is needed to 
finish off the burning, thereby requiring a high heat in the 
regenerator^ which is amply provided by Mr Dunnachie's method. 
One of the chief causes of failure on the part of every person who 
attempted to bum bricks by the use of gas before the Glenboig kiln 
was brought to a practical success, was a want of the proper dis- 
tribution of gas and air throughout the burning chamber, as also a 
proper admixture of the gas and hot air at every point. At one 
place the bricks would be roasted, while at another they would be 
under-burned ; in the Glenboig kiln, on the other hand, there is no 
burning in streaks of hard and soft bricks, as there is an even dis- 
tribution of heat throughout the whole mass of the bricks under fire. 
The Hoffman kiln is continuous in its action, and is worked on the 
principle of heat-regeneration, but the fuel used in it is small coal, 
which requires to be fed in from the top. No doubt, the kiln in 
question is very serviceable where the bricks can be burned by 
employing a moderate heat ; but it would not serve for burning re- 
fractory fire-bricks, which require a high melting heat. One disad- 
vantage attending the use of the Hoffman kiln is the tendency which 



216 On a Coniinuous 

certain earthy constituents of the coal have to form fusible silicates 
with the clay, many of the bricks being wasted in the burning 
operation by being fluxed. That difficulty never arises where 
gaseous fuel is used. Owing to the fact that the Glenboig kiln is 
under such perfect control, it may be advantageously employed in 
burning the most refractory fire-bricks, even ganister bricks, and 
down to common red bricks. While speaking of the fluxing 
of bricks by the use of solid fuel in ordinary kilns, it may be 
stated that the walls themselves also suffer seriously from the same 
cause, whereas the kiln under consideration seems scarcely to 
suffer at all from tear and wear. 

In addition to the extensive adoption of this new kiln at the 
Glenboig Company's own works, progress has been, or is being, 
made in the way of adopting it elsewhere, the interest excited in 
regard to it being very great, as is evidenced by the fact that almost 
all the leading firebrick manufacturers of the kingdom have either 
visited the works themselves or have sent responsible representatives 
to inspect the new kiln in operation. It is in use at Gaiiikirk burn- 
ing fire-clay goods. At Tamworth, it is being used for the well- 
known Staffordshire blue bricks, and in this case there are same 
facts of very special interest, as they show how the kiln can be 
adapted to new circumstances. The raw coal is distilled or car- 
bonised in ordinary gas retorts, and the by-products are collected 
and subsequently treated separately, while the gas which is obtained 
is used in firing the brick-kiln. It is got without the use oF a 
separate producer, and as it contains no air it has probably five 
times the calorific or fuel efficiency of ordinary producer gas. The 
residual coke that is drawn from the retorts is a good marketable 
commodity. As evidence of the confidence which the proprietor of 
the Tamworth Coke Works has in the efficiency and economy of the 
Glenboig gas kiln, it may be stated that he has recently completed 
negotiations for the erection of another complete kiln of ten cham- 
bers. In another kiln of the same sort erected at Sheffield, Messrs 
Lowood & Co. are successfully firing their famous ganister bricks. 
Messrs Henry Sharp, Jones, A Co., of Poole, in Dorsetshire, are 



Regeneraiive Gas Kiln. 217 

now erecting a set of ten chambers for firing sewerage pipes. Not 
only is the kiln in this instance identical with that first erected at 
the ^^ Star " Fire-brick Works, but it has, in addition, an arrange- 
ment for the economical introduction of the common salt required 
for glazing the pipes. A kiln such as we are speaking of was 
erected sometime ago at the Rutherglen Pottery, the proprietor of 
which declined to accede to the suggestion of the patentee to con- 
struct a muffle within each chamber so that the ware in course of 
being fired might be completely protected from the direct action of 
the flame and heated gases passing through the chamber. As might 
have been expected, the ware, coated with its delicate glazes, did 
not '^ stand fire " under such conditions, and the use of the kiln for 
firing pottery was suspended ; but as Mr Dunnachie is confident of 
the ultimate success of the kiln for firing either earthenware or 
porcelain, when his valuable suggestion as to the adoption of a 
muffle is acceded to, he does not regard the Butherglen example of 
his invention as having been '^put on the shelf" in perpetuity, but 
simply as being in abeyance in the meantime. The peculiar adapt- 
ability of the Glenboig kiln is abundantly shown by the great range 
of firing temperatures that may be got in it, extending from that 
which suffices for the Tamworth blue bricks, which is far below that 
required for burning fire-bricks, up to that which is needed for 
Sheffield ganister bricks — being almost as great an extreme in the 
other direction. 

As an invention in connection with sanitary improvement in 
industrial districts, the Olenboig gas kiln ought to take a very high 
place; indeed, with smoke-prevention advocates, it has already 
gained such a position, from the fact that its general adoption in 
brick-making and pottery districts would reduce to a minimum 
smoke nuisance in many places that have acquired an unenviable 
notoriety for polluting the atmosphere. There is no breach of con- 
fidence in saying that the Duke of Sutherland, Lord Whamcliffe, 
Sir Thomas Bra&sey, M.P., and many other persons of greater or 
less eminence, and who have large industrial interests at stake, are 

now giving attention to the Glenboig gas kiln, on account, in 

29 



218 On a Continuous 

some measure, of its intimate comiection with the preyention of 
smoke. 

There are many directions in which the use of this kiln is attended 
with economical results. Some of these have already been incident- 
ally mentioned or alluded to, yet still one more may be adduced ; 
it is in the kind of coal from which the required gaseous fuel may 
be obtained, for even the commonest or least valuable slack or dro^ 
amply suffices as the source of the gas. Furthermore, if we tab 
weight for weight, a very much less quantity of it is needed when 
compared with what is necessary to do the same amount of work in 
an ordinary coal-fired kiln, in which, by the way, good round coal 
at a high price has often to be used. 

It will serve a good purpose ii' I now lay before the members of 
the Institution one or two most reliable facts bearing on the rel&tire 
fuel-economy of this kiln. At the request of the Directors of the 
Glenboig Union Fire-Clay Company, the managers of the several 
works recently made careful observations, and without any collusion 
with each other, in regard to the consumption of coal for firing pur- 
poses, over a period of some six or seven weeks, with the different 
kinds of kilns in use. The data obtained from the separate reporu 
of the managers show that the average cost of fuel used by the New- 
castle kiln was 8s 2d per 1000 bricks burned; that the cost of fuel 
used in the hopper kiln, invented by Mr Dunnachie about twenty 
years ago, was an average of 6s 6Jd per 1000 bricks ; and that the 
average cost of the fuel used in the form of gas, in what has alreadj 
been called the Glenboig kiln, did not exceed 2s 9^d per lOOO 
bricks burned. 

Mr Frederick Siemens, who was long and intimately associattnl 
with his distinguished brother, the late Sir William Siemens, id 
connection with heat-regenerative furnaces, &c., has become so pro^ 
foundly impressed with the merits of this gas kiln that negotiations 
are in progress between his firm and the patentee, with the view of the 
former undertaking its introduction into various industrial district 
at home and abroad, in conjunction with the newest form of Siemens 
gas-producer, which is doubtless well-known to many of the memb«& 



Regenerative Oas Kiln, 219 

Keferring with a little more detail to thia producer, it may be said 
that a jet of steam is introduced into the generator chamber in 
order to give the gas a slight '^ push/' though it is stated that ex- 
perience gained in some recent cases, shows that such a device is npt 
actually necessary. In it '' clinkering " is reduced to a minimum, if 
it is not practically altogether m7; and as no stoppage is required for 
cleaning operations, one generator will suffice for a kiln of ten 
chambers, whereas, up to the present, two producers have always 
been considered necessary. 

In conclusion, I may be permitted to say a few words in regard to 
the relationship which this gas kiln bears to the Thomas-Gilchrist 
or basic process of making steel, a process which will doubtless soon 
bulk largely in this part of the kingdom. After having under- 
taken the sole manufacture in Scotland of the basic bricks for 
lining the steel converters, Mr Dunnachie found that an enor- 
mous expense would attend the firing of such bricks if raw coal 
had to be used as the fuel, as they would need quite a steel-melting 
heat ; and it may almost be said that the necessities of the case 
led to the construction of the continuous regenerative gas kiln 
treated of in this paper, which is almost the first formal com- 
munication that I have had the honour and pleasure of making to 
the Institution. 

In inviting discussion on the paper, 

The President said he was sure all present had listened with 
pleasure to the interesting and instructive communication. 

Mr K K£MP had really great pleasure in listening to the paper 
on what appeared to be a really efficient invention. At the begin- 
ning of the paper it was stated that the kiln practically utilised all 
the heat that was in the gas, but that there was still sufficient 
escaping to give draught enough to pull the waste gas up the chimney. 
Perhaps Mr Mayer could tell them what temperature there was in 
the chimney to cause that draught, as it must be a percentage of the 
total beat. 



On a CofUlntious 

Mr Mater replied, that the chimney at Olenboig was used for 
other kilns besides the regenerative kiln. Not only did it do the 
work of that kiln, but also of some of the other kilns in the 
works, so that the heat in it was not due to the former entirely. 
He was not aware whether the temperature in the chimney had 
been tested, but as Mr Dunnachie's son had had three years' 
training in a laboratory in the City, and was devoting some 
attention to the production of a really serviceable pyrometefi 
iiomething would doubtless be done in that direction by-and-by 
One main point, he repeated, was that practically there was no 
waste heat. 

Mr Kemp said from the explanation given it was apparent that 
the draught in the chimney was kept up by other fires, and not by 
the escaping gases from the regenerative kiln. 

Mr Mayer rejoined that the chimney had certainly to do other 
work. 

The President recollected well the Hoffmann kiln for burning 
bricks, which had been erected at Belfast a good many years 
ago, and which he had frequent opportunities of visiting. The 
economy of heat in that kiln was remarkable, so much so, in 
fact, that it became necessary rather to throw away a little more 
of the heat purposely because the chimney was too cold almost, and 
the moisture evaporating out of the warmer damp bricks condensed 
upon the cooler ones, and so the economy was carried a little too 
far. Probably Mr Mayer had something to tell them on that subject 
in regard to this new kiln. 

Mr Mayer said that the arrangements for getting rid of the 
escaping vapour in the steaming process were very perfect. The 
chamber in which the steaming operation was carried on was actually 
cut off from all the others. The vapour escaped through the crown of 
the chamber by some fifteen openings, and special means were taken 
to increase the activity of the current from the chamber during the 
steaming stage. 

Mr S. G. 6. GoPESTAKE noticed that in the model shown the crown 
was semi-circular and in the drawings on the wall somewhat flatter 



BigiTtercUive Gas KUn. 221 

He wished to know whether or not the shape had anything to do 
'with, the effectiveness of the kiln. 

Mr Mayer said Mr David Johnston, who was to some extent 
responsible for the diagrams, might be able to answer that 
question* 

Mr Johnston explained that Fig. 1 was merely a ground plan, 
bat that there was a longitudinal section in Fig. 4, Plate XVIII. 

Mr CoPESTAKE was anxious to find out if there was anythin 
special in the shape of the arch. 

Mr Mayer did not think there was any essential element in the 
shape of the arch. 

Mr Kemp thought the half- circle was better suited than the other 
form for the purpose in view. 

Mr Johnston wished it to be understood that in the diagrams 
he had merely followed lithographed drawings, given in the patentee's 
*' blue book." 

Mr Kemp was of opinion that the model showed the ordinary 
arch. 

Mr Mayer believed that the model might show a more recent 
method than the diagrams, and that the semi-circular arch might 
give better results than the flatter one. 

Mr James M. Gale observed that there was less lateral thrust in 
the semicircular than in the other form of arch. 

Mr Geo. Eussell asked if men worked in the drying stove at 
a place indicated by him 1 It appeared to be a hot place, especially 
in summer, with furnaces below, and its roof of iron. 

Mr Mayer replied in the affirmative, explaining that he had 
referred to it as the moulding floor. 



222 On a Can&mums 

The discussion of this paper was resumed on 28th April, 1885. 

On the call of the Chairman, 

Mr F. W. Dick said he had not been able to be present at the 
last meeting to hear the paper read, nor had he been able to find 
time to peruse it since ; but he knew something of Mr Dunnachie's 
plans. Of course anything which utilised heat, instead of allow- 
ing it to radiate into space, must be good. On the whole he 
thought the plan an excellent one, but he would prefer to saj 
nothing more at present, as he was ignorant of the contents of the 
paper. 

Mr Henry Dyer simply wished to remark that as Mr Mayer's 
paper was descriptive of an invention, which seemed to be correct in 
principle and successful in practice, there was not much to be said 
about it in the way of discussion. The chief duty incumbent upon 
them on that occasion was to thank Mr Mayer for his excellent paper, 
and to congratulate Mr Dunnachie on his marked success. Perhaps 
he might be allowed to suggest that a few simple experiments should 
be made with the oven to ascertain if it was working under the condi- 
tions of maximum efficiency. These were — ^first, that there should be 
little or no external radiation ; second, that the combustible gases 
should be consumed; and third, that the temperature of the chimney 
should be just sufficiently high to carry off the waste gases. In the 
oven described he thought that the chimney served for other pur- 
poses, so that it might be somewhat difficult to carry out some of 
the experiments, but he had no doubt that Mr Dunnachie would 
be able to ascertain the actual efficiency of his invention. In 
concluding, Mr Mayer had remarked that this was the first paper 
he had read before the Institution; but for his own part he 
hoped, now that the author had made a start, he would give other 
papers of the same class, especially as the Transactions of the 
Institution in the past had been somewhat deficient in papers 
relating to applied chemistry and metallurgy. Of course they knew 
that Mr Mayer had paid special attention to these subjects, and 
he would confer a great boon upon the members by supplying 



Regenerative Gas Kiln. 223 

them with particnlars of recent advances in these departmentSy 
especially in the industries connected with Glasgow and neighbour- 
hood. 

The Chairman (Mr C. C. Lindsay, Vice-President) said he had 
not the pleasure of hearing Mr Mayer read his paper, neither had 
he read it in the Transactions, but it was a class of paper — bearing 
upon the economical use of fuel — which he would like to see more 
of. He was not acquainted with the burning of fire-bricks and 
pottery as described, but he had some experience of steel making 
with gaseous fuel, and it seemed to him that Mr Dunnachie had 
been very successful so far in his work. He hoped Mr Mayer 
would, as Mr Dyer had suggested, give more papers of a similar 
class in the future. 

Mr Mater said with regard to the remarks made in the discus- 
sion, it was Mr Kemp, he thought, who referred to the chimney 
at the Glenboig Works doing more than the work of the simple 
kiln or set of ten chambers to which it was specially attached. 
In regard to that, Mr Dunnachie had informed him that some 
of the kilns which had been erected in England were doing work 
only into one chimney stalk, and that each chimney stalk was 
doing the work of only one set of chambers, so that doubtless some 
specific details might be got in the course of the next few months 
as to the results in one or more of those instances. He had no 
doubt Mr Dunnachie would be quite willing to receive a Committee 
of experts from the Institution, and make preparations for them 
carrying out certain observations, if that should, in the opinion of 
the Council, be deemed desirable. As Mr Dyer seemed to be 
much interested in the subject dealt with in the paper, he (Mr 
Mayer) suggested that that gentleman might act on that Com- 
mittee. The question had been raised by Mr George Russell 
about the rather hot quarters that the brick-moulders and their 
attendants would have, working in the drying stove, shown in 
Fig. 2, cross section. But it must be remembered, however, that the 
drying stove was some 60 or 70 feet long, and extended not only 
over the open space between the two rows of firing chambers, but 



224 On a CorUinuaus 

over those two rows of firing chambers themselves, so that while a 
drying stove, it could also be fitly employed as a moulding room, 
for the ten chambers were not all equally hot. The brick-moulder 
could, therefore, moving his moulding table about at pleasure, always 
have a cool place to work in, even in the height of summer. Then, 
lastly, with reference to the point raised by Mr Copestake about the 
arches of the kiln being flat rather than semi-circular. It would be 
remembered that the arches were flat in one of the diagrams shown 
at last meeting and semicircular in the model, which was now in 
the Inventions Exhibition in London. In the plans as originally 
drawn out the arches were semi-circular; but the diagram was 
copied from the patent specification drawings where they were 
given flat by mistake by the patent agent without the knowledge 
of the patentee or inventor. The arches were, therefore, semi- 
circular from the first, thus securing what Mr Gale desiderated— 
the utmost strength possible. Personally he could assure them that 
some of the chambers he had seen lately had borne the test of age 
and experience without giving way in the slightest particular. In 
his opinion they had great durability and power of resisting wear 
and tear. The suggestion Mr Dyer had thrown out would, he 
hoped, be acted upon, so that the Committee might report to next 
Session of the Institution what had been done. 

Mr DvER thought Mr Mayer had mistaken Us meaning. He did 
not propose that the Institution should appoint a Committee, because 
if they once commenced that they would have plenty of work to do. 
It was Mr Dunnachie's business, he thought, to make a few simple 
experiments, and give the results to the Institution. Of course, 
there was nothing wrong in such a proposal, but there were other 
important matters that equally required investigation at their hands, 
and if the Council took up such things they would have more than 
enough to do. 

The Chairman asked Mr Mayer if he had anything further to say 
in view of Mr Dyer's remarks. 

Mr Mayer replied that he had nothing to say beyond this, thut 
he was quite willing to bring up a report in the shape of results. 



Begeneraim Gas Kiln, 225 

tested as far as he was able to test them, and that he would do 
his best to collect information on the subject in question from 
those persons whom he had referred to in the paper as using the 
regenerative gas kiln. 

The Chairman said he had much pleasure in proposing a hearty 
vote of thanks to Mr Mayer^for his^^paper. 



80 



On ike BuU Fastenings of Iron Vessels. 
By Mr Stavbley Taylor. 



SEE PLATE XIX. 



Beeewed iStd February; Read 24th March, 1885. 



Mt desire in this paper is to draw attention briefly to the question 
of butt fastenings as at present ordinarily applied in the structure of 
iron vessels. 

In introducing this subject, I am sensible that it is not altogether 
new. As, however, there have not recently been many papers 
before this Institution dealing directly with the practical questions 
of ship construction embraced by this subject, I trust the matter 
may still prove of some interest. For myself, I believe it to be the 
v'Ual point as regards procuring a perfect structure, and I hope 
therefore it will be thought worthy of further consideration. 

The main object, from a commercial point of view, in the design 
of any iron structure, ought to be to get a maximum strength on a 
minimum of material. In a merchant ship, where weight of hull 
bears such a direct relation to the freight-earning capabilities of the 
vessel, the item of weight is a primary factor to be considered. 

My contention is, that if we are to get the full value of the weight 
of material employed in building a ship, some reformation is wanted 
in the custom of securing butts from that at present observed in 
shipbuilding practice, and this to the effect of getting increased 
fastening. 

I do not think it is an exaggeration to say that, after a little 
service, a considerable proportion of vessels, particularly those of 
large dimensions, ''show the butts" of their shell plating amidships. 



22H On the Butt Fasteningi 

Observation at the graving docks and slipways of oar various ports 
makes this only too obvious. If these ships conld be built of the 
same scantling, or perhaps a considerable percentage less, and made 
a wholt^ jointless mass, their efficiency and immunity from fault of 
this nature would be unquestionable ; but as the weakest part is thi" 
index of the whole strength, the butt gives way — it may be merely 
to the extent of being '^ paint cracked " — but, whatever the extent, 
it is undoubtedly due to a weakness, local or otherwise, which, 
showing first at the butt, proves it to be the most vulnerable part. 

I do not assert that this ^'showing" of butts is a really dan- 
gerous defect. Many vessels whose butts show perhaps badly after 
their first voyage, if carefully treated never subsequently appear to 
get any worse, their structural strength, as a whole, being ample to 
resist further aggressions and to meet all work to be done. There 
are, however, many cases where this showing of butts is first ob- 
served, in which the vessel is either doubled or strengthened and 
loaded with additional weight, much to^the commercial disadvantage 
of the ship. 

It is manifestly evident that to load a ship with great weight of 
scantling with the view of gaining increased strength is in principle 
wrong, unless the fastenings are correspondingly increased in propor- 
tion to the added section. A ship may be, and many are, built 
with excessive and extra weight of material and insufi&cient ^opor^ 
tionate butt fastenings. Such vessels may do their work well, but 
this can only be due to the fact that the strength at the weakest 
point is sufficient to do the work required, and all weight above this 
requisite working strength is carried uselessly and to the exclusion 
of freight-earning cargo. 

It has been frequently demonstrated that chain riveting is the 
most efficient method of butt connection. Assumed, then, that a 
butt is built in this manner, with the most approved proportions of 
rivet area to plate section, and together with good workmanship 
made as efficient as the means will admit. Such butt if subjected 
to a steady tensile strain would probably bear without fault a much 
greater strain than we can imagine it would ever have to' meet in its 



of Iron Fmels. 229 

place as part of a ship's structure ; but the fact remains that ships 
are built with such well*arraDged butts, yet still give trouble in the 
manner indicated. The cause I assume to be — ^where it cannot pal- 
pably be traced to inherent structural weakness — a local panting, a 
continual tremor or vibration, due to the sudden varying strains a 
ship is subject to in a seaway ; to the working of heavy machinery, 
or to successive blows from waves and heavy seas. This tremor^ 
reverberating on each plate as cin individual and separate mass in 
itself, must be exhausted at the extremities. So the movement 
thus created — even in the closest fitting butt — has a tendency to 
start the caulking and cause the defect complained of to be ob- 
served ; leakage and consequent corrosion unavoidably follows. In 
badly fitting butts, though they may only happen to be a small degree 
open when originally riveted, this action must operate more quickly, 
and the fault consequently becomes aggravated. Perhaps, on the 
whole, steamers are more readily affected in both these respects than 
sailing vessels, their dimensional proportions and motions at sea being 
more severe — the vibration from their machinery in itself, in some 
cases, being no doubt sufficient to cause the defect without co- 
operation from other causes. 

Upon the assumption of butts cracking from this latter cause, it 
may be argued that the same defect should also show at the land- 
ings, and that no plate butt, however well proportioned, will ever 
and at all times be safe from the defect. No doubt both forces more 
frequently, and in a greater or less degree, are acting simultaneously ; 
but it will be obvious that the strains affecting the plating will gene- 
rally be much more severe upon the ends than upon the edges of 
the plates, and that any vibration will also be more acute at the 
termination of the greatest dimension or length of the plate rather 
than at the smaller dimension of breadth. The disposition of the 
caulking, being upon the edge of the plate, in the case of the landings, 
may probably have a better effect to resist movement from vibration 
than face caulking has. 

I have, therefore, to urge the fitting of double or outside and 
inside butt straps as a remedy for the evil, and as a simple means of 



230 On the Bull Fasknings 

securing increased strength and efficiency without serious inereaae of 
weight. The proposal can, of course, have no claim for oiiginalitj. 
Indeed it is mostly upon old ships that we find double straps fitted, 
they having either been put on subsequent to the vessel's completion 
to cover defective butts arising from the causes named, or in some 
isolated instances, perhaps, fitted originally with a view of securing 
greater efficiency. Lapped joints are also in a few cases to be met 
with, in fact the practice is at the present time still occasionally 
adopted by some East coast builders. This is not, perhaps, a system 
that it would be advisable to adopt throughout in a ship's structore; 
it might, however, be used for some parts of the plating and some 
inside work, but it can in no case be considered so effective as doable 
or even single straps, the strength of the butt under conditions both 
of tension and compression being dependent alone upon the shearing 
resistance of the rivets. This may, however, be somewhat equalised 
by increasing the rivet area. 

The main objection to both practices is, I suppose, ^'unsightliness." 
There will also be the objection of increased friction or resistance 
due to the projecting strap edges, and the liability of the straps — 
particularly those of the outside strakes — to be chafed against dock 
walls, Ac. I do not, however, think any of these worthy of great 
weight when the advantages gained are considered. If by any 
means butts of shell plating can be made never to require attention 
after a ship is once built, and when the saving of trouble and ex- 
pense this would be each time a vessel is docked is realised, the 
objection of unsightliness will, I think, soon be banished, and I 
take this to be the most general objection. To what actual extent 
frictional resistance would be increased by outside straps is a point 
upon which any information would be valuable. 

There can be no doubt that the simple transfer of the caulking 
from the face of the butt to the edge of the butt strap, which outside 
straps would involve, would do much to dispose of the evil of 
*^ paint cracked" butts; and thus, apart from strength, outside 
instead of inside straps would be a direct advantage. This advantage 
would also follow the adoption of over-lapped butts. 



of Iron Fesstk. 381 

The outside atraps need not of necessity be fitted fore-and-aft 
over the whole plating; in most cases, probably a limited distance 
amidships would be quite sufficient. Nor need the outside straps be 
made thicker than from one-half to two-thirds the thickness of the 
plating itself, with the edges of the strap chamfered down to a bare 
caulking edge. In treble-riveted straps, as the pitch of rivets in the 
back row is too wide to ensure a firm caulking edge for the outtfide 
strap, the cover strap need only extend to the second row of rivets 
on each side of the butt 

The systems of double straps or over-lapped butts would apply to 
the ordinary in-and-out and clinker method of plating mostly in 
vogue ; but the system of flush edge-and-edge plating, with outside 
cover seam strips, which is now becoming so general, might be ar- 
ranged in a different manner. This method of plating cannot be 
too strongly recognised as the best that has yet been devised to 
equalise the strains both on plates and rivets, though it unfortunately 
has a disadvantage in these days of competitive economy of being 
more expensive than the common practice. I would suggest for this 
system a slight departure from the usual custom of butt fastenings, 
and it is merely to leave the butts of the outside seam strips about 
three-quarters of an inch wide, or sufficiently far apart to admit of 
the plate ends being caulked against the edge-and-edge plating, the 
usual straps of course being fitted inside. The butts of the flush 
edge-and-edge inside plating to have double straps. With this ar- 
rangement no butts ought ever to give trouble, provided the whole 
structural strength is sufficient. 

I do not suppose I shall get many to agree in advocating a reduc- 
tion of scantling from that at present in use, and in this matter I 
refer solely to the requirements of the various classification Segistries. 
It is not a question to be only casually treated, and I do not propose 
in this paper to trespass very far. The two subjects are no doubt 
very closely allied, but I will now only venture an opinion, that with 
more attention to the means of fastening the many parts of a ship's 
structure together, and a more careful distribution of material, some 
reductions might be considered. The tendency, however, lately 



232 On the BuU Fastenings 

has been aU in the way of increase and greater weight. It is not 
asserted that while these increases in scantling have been made that 
butt connection has been entirely ignored. Moderate increases 
have been enforced in this respect also, but had these increases in 
riveting requirements been made earlier, the necessity for addi- 
tional weight would probably never have arisen. I may here 
mention that Mr Henry H. West, chief surveyor to the Liverpool 
Underwriters' Begistry, has called special attention to this matter 
in a paper read by him before the Institute of Naval Architects 
last year. 

In the consideration of reduced scantling the element of " stiffness *' 
has to be taken into account, and it is said that this has been dan- 
gerously encroached upon in some steel vessels built with the 
reduced scantling sanctioned for that material This is an important 
point and one to be duly guarded against, but I look almost entirely 
to better butt fastenings as the most immediate means of balancing 
any apparent difficulties in the way of reducing weight of scantling. 
What the particular observed results of this flexibility have been I 
hav^e not been able to learn ; any details would be of interest. 

It is at all events an anomalism that rules should be framed to 
specify certain sizes of material for a certain ship and certain hutt 
riveting, say double for this required thickness, but in the case of 
another ship, whose scantling is by rule the same, additional 
riveting — treble or quadruple —is required on account of some dif- 
ference in the ratio of her proportions of length, breadth, and depth. 
The section of each plate used i<3 the same in each case ; why its fall 
strength — represented in the latter case, we must presume, by the 
treble or quadruple riveting — should not be maintained in the first 
case is a palpable inconsistency. If it is not required in the one, 
then obviously the scantling may be reduced more proportionate to 
the strength of the butt, and retained, if it is needed, in the other. 
To some extent, no doubt, this will be found in the application of the 
rules to adjust itself, but there are many possible and actual instances 
where such adjustment does not occur. The inconsistency iu these 
cases can only be condemned. A similar discrepancy also occurs in 



of Iron Vessels. 288 

oaing the same size of rivet for varying thicknesses of plate ; in this 
case the rivet area remains constant while the plate section increases 
Trith each thickness. The question of varying the size of rivets in- 
volves practical difficulties which it is perhaps better^ if possible^ to 
try and avoid. 

In order to show the relative proportions which rivet area bears 
to plate section in butts, double, treble, and quadruple riveted, of 
plates varying in thickness and width, tables giving these results 
are annexed hereto. See Tables L, II. and III., Cols. 11 and 12. 
Also in Cols. 18 and 19 are given the percentages of strength of 
plate over rivels, or rivets over plate, as the case may be, calculated 
upon the basis of 20 tons as the breaking strain per square inch of 
the plate, and 18 tons as the shearing strain of the rivet In these 
circulated results the full efifective value of the rivet hammered — 
that is, yV^^ ^^ ^^ ^^^^ larger than the cold rivet — ^has been taken 
and 17 per cent., or |th has been assumed as a fair average to be 
added to the section punched out of plate at row of rivet holes for 
a good countersink. A countersink with a face diameter of one and 
a-half times the diameter of the rivet will be equal to 25 per cent. 
more than a parallel hole, and 17 per cent, may therefore be con- 
sidered too low an allowance. This factor was determined upon 
after measuring the countersinks adopted by a number of builders, 
so that it may be considered very closely to represent the general 
practice. As, however, in these calculated results the per centage 
has been admitted over the whole row of rivet holes, assuming them 
all to be countersunk, which will not actually be the case as regards 
the landing holes for an inside strake, the proportion will be 
somewhat raised. 

The arrangement of butt rivets, upon which the tables are based, 

is such as would be adopted on the inside shell plate of a vessel's 

hull (see Figs. 1, 2 and 8, Plate XIX.), and the widths of plates 

comprise those most commonly in use. The exact rule spacing of 

four diameters cannot, of course, be correctly applied for constant 

widths of plate and varying diameters of rivet In Tables I., IL, 

and III. the widths are made to suit the exact four diameter 

81 



234 OnOeSfUiFasiefimgs 

spacing. Where this cannot absolutelj be applied the neaieol 
practicable division has been made ; but it will readily be seen that 
any increase in the width of plate, however slight, will affect the 
rivet area adversely to the comparison of plate section, without 
materially affecting the rivet spacing. 

In Table lY. a constant width of plate of 48 inches has been 
taken, and results given for the nearest division of rivet spacing, 
both above and below the four diameter spacing, the resolts show 
differences varying from 6 to 8 per cent, in the value of the rivet 
areas. 

For yV ^^^ kV plAtes the Underwriters' Registry require {i" and 
1' rivets respectively, against }* and I" required by Lloyda'. 
These distinctions are given in the tables, and the result appears all 
in favour of the larger rivets. With these exceptions, and within 
the compass of the tables, the requirements of both societies are the 
same. 

The inside plate having a completely strapped butt^ has been 
chosen for comparison in preference to the outside plate, whose butt 
strap^^ztending only from edge to edge of the adjoining inside 
strakes — ^is incomplete, the rivet strength of the butt, consequently, 
is less than that of the inside strake. 

The rivet area, therefore, in this comparison, appears more 
fskvourably than would be the case at any other butt strap in the 
ship. 

In these considerations, assuming the strap for treble riveting to 
be xV ^^ ^^ ^^^ thicker than the plate connected, and for quadruple 
riveting to be ^^ thicker, the butt strap may be ignored as the con- 
ditions are either equal or favourable to the strap. 

The values arrived at in the tables, beyond and including col. 13, 
are not advanced as final ; they can only be considered as purely 
theoretical, and determine merely the apparent results for the values 
of material used in the ratio upon which they are based* 

The true shearing stress of the rivets and the tearing strain of the 
plate can perhaps never be accurately ascertained for such butts as 
we are here dealing with, on account of the impossibility of distri- 



of Iron Fesuls. 235 

bating the load eqoallj over the whole area of material under stress. 
The friction of surfaces, as affecting the result, is also an element upon 
which very little is known. 

The tables require little further explanation. From the results it 
may be deduced generally that the smaller thicknesses of plate, say 
up to j^, may be safely fastened at their butts with double riveted 
straps ; that plates from ^ to {^, except for excessive widths, ought 
to be treble riveted ; and that plates of {^ and above, and of ex- 
cessive width above |f , ought to be quadruple riveted. By fitting 
doable straps these limits might be considerably increased. 

On comparing col 16 of Tables I. and II., it will be seen that the 
relative result of butt strength for double and treble riveting is 
actually the same, because in the treble butt the strength of the 
plate at AB is increased by the shearing resistance of the back row 
of rivets, CD (Fig. 2), and the total shearing strength of the rivets is 
only increased to a like extent over the double riveting. The per- 
centage of strength is, of course, in favour of the treble riveting, as 
the value respectively of the plate and rivets is increased, though 
the nett result appears the same. 

If the full complement of rivets be inserted in the back row, the 
rivet value becomes increased to the extent of one-half more than 
the double riveting, while the plate strength remains constant. 
But by ordinary treble riveting the strength of the plate at AB, 
plus the back row of rivets, approximates very closely to the strength 
of the plate through the line of frame holes YZ, which is the normal 
strength of plate (see cols. 14 and 21, in Table II.) : therefore, by 
increasing the back row of rivets to a complete row, we at the same 
time reduce the plate strength and gain no advantage. Consequently, 
we must look to increasing the rivet value without interfering with 
the plate strength, and this can only be done, either by adding an 
entire extra row of rivets, as in quadruple riveting, or by putting 
the rivets in double shear by using double butt straps. A difficulty 
in the way of the general adoption of quadruple riveted butts arises 
from the fact that the increased width of straps necessary will entail 
a somewhat wider spacing of frwmes, particularly for the larger sizes 
of rivets. 



236 On the Butt Fastmngs 

It may be urged that doable straps mean additional expense, but 
any small apparent outlay in this respect will be more than met bj 
the saying in weight which must follow any system which establishei 
a normal strength on a uniform basiB throughout the whole structurew 
The efficiency thus secured will in itself be synonymous with economy. 
With attention to this matter iron may still perhaps be consi- 
dered to compete more favourably with steel ; for in steel riveting 
where the shearing resistance of rivet steel falls so much below the 
tensile strength of steel plates, the plate limits for riveting, as 
given above, would require to be reduced proportionately, unlea 
the rivet area be increased in a corresponding ratio. This diacrep- 
ancy in the shearing resistance of iron and steel rivets, compared with 
the tensile strength of their respective plates, when taken full 
advantage of, puts the two materials, considered as constructife 
competitors, on a slightly more uniform footing. 

Table Y. records the results of some shearing tests on rivets in 
single and double shear, comprising lap joints, butt joints with 
single cover straps, and also with double cover straps. The mean of 
the single shear tests is 17*56 tons per square inch of rivet area for 
hand riveting, and of the double shear, taking the single area of 
rivet only, 31*6 tons, which gives a value in shearing resistance to 
the rivet in double shear, rivet for rivet, of 80 per cent, more than 
the rivet in single shear. The corresponding figures for hydraulic 
Vivetiug are 19*13 tons, 83*5 tons, and 75 per cent respectively. 

Endeavour was made with some of the samples to observe the 
exact portion of the load at which slipping commenced, and this was 
found to vary for hand riveting from about 10^ to 33^ per cent of 
the total stress, and for hydraulic riveting from about 27 per cent, 
to 40 per cent — a very wide divergence indeed. 

Professor Kennedy, 'in his investigations into the strength of 
riveted joints of steel plates and steel rivets, states that by the aid 
of a magnifying glass, slip was observed to commence at about 
one-tenth of the breaking load, and that it was visible at about one- 
fourth of the load. 

There is an average difference between the shearing results of the 



cflfWk Vesseb, 2S7 

riTets riveted hj hydraulic power and those riveted bj hand, 
favourable to the former to the extent of from one to two tons. 
This, is no doubt due to increased friction, and to the holes being 
better filled by the greater pressure brought to bear upon the rivet, 
which tends to prove the great superiority of power riveting over 
hand work. It must also have been due to some varying in the 
effectiveness of the riveted work which caused the proportion of 
load at which slip occurred to be so irregular. 

One point is brought out prominently in considering the small 
percentage of the ultimate shearing stress at which slip commences ; 
and it is, that at comparatively low strains it is a reasonable in- 
ference that slip will occur to an extent sufficient to start the slight 
face caulking which an ordinary shell butt receives, and so permit 
leakage and corrosion to begin. Also, that this will occur without 
materially affecting the rivets under strain ; for, after slip was ob- 
served in the test samples to have begun, the weight was removed 
and the rivets found to be perfectly sound — the elasticity in the 
material and joint having recovered itself on the strain being re- 
lieved. This was especially noticeable in the pieces riveted^ by 
hydraulic power, for in some instances as much as 70 per cent to 80 
per cent, of the total load was applied — the slip measuring about 
one-eighth of an inch — and the rivets on being tested after the 
weight was removed were found sound. In the hand-riveting the 
rivets were generally slack after about 50 per cent, to 60 per cent, of 
the load was applied. 

Under ordinary circumstances, it is a remote supposition that the 
rivets in a butt of shell plating would shear or the plate fracture, 
except at the sheer strake where the top edge of the plate is un- 
supported. In the body of a ship each plate is so supported 
and assisted by the adjoining plates and overlaps of the landings, 
that any failure must be general. Indeed, from actual fact, it 
must be admitted that we more frequently find in cases of absolute 
failure that the plate has torn while the rivets remain intact; and if 
this is accepted as final proof that the present practice is sufficient^ 
the object of this paper is useless. But I submit there is the danger 



288 On ike Butt FatUntngi 

of the rivets in a weak butt working adrift or admitting of dip in 
the butt^ sufficient to entirely destroy the real value of the riveted 
work, as constituting a solid joint, and so to throw an undue and in- 
tensified strain on the plates immediately adjoining. With straiiis 
ever varying in point and direction, such as we have to contend 
with in designing the structure of a ship, I think that it is desiraUe 
we should endeavour to increase the margin of safety as much as if 
consistent, and to make the structure as complete as possible by 
treating each plate and point of connection upon its own individual 
merits. 

I would suggest, before closing this subject, that the riveting in 
the fore-and-^ plate landings in many cases is out of prop(MrtioD 
to the riveting requirements for the butts, and might with prudence 
be somewhat reduced. 

Fig. 4 (see Plate XIX.) is a scale which shows at a glance the 
rivet area in square inches, corresponding to any plate section np to 
60 square inches, in the proportion of 20 tons, as the tensile strength 
per square inch of the plate and 18 tons as the shearing strength of 
the rivet. 

To sum up the whole, my conclusions are that butt riveting 
should be wholly dependant upon the thickness or sectional area of 
the plates connected, and not upon any dimensions or proportions of 
the vessel ; that butt riveting in relation to the thickness or section 
of plate ought to be considerably increased from present practice ; 
and that the most efficient method of securing strength of joint ii 
by using double butt straps. 



of Iron Vessels. 



239 



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of Iron Vessels. 247 

In the after discoBsion, 

Mr BoBBRT Mansel said he entirely agreed with nearly every 
deduction arrived at in this paper, and he had on his memory an 
instance of a case which went to show that it would be of great 
importance to improve butt fastening by introducing outside as 
well as inside straps. In 1858, the once well-known steam vessel 
'^ Persia/' after some heavy transatlantic passages, gave decided 
indication of being deficient in longitudinal strength, and it became, 
necessary to arrive at some definite conclusions as to the amount of 
additional strengthening required. This vessel was heavily plated 
on the bottom and sides up to the main sheer, but the 'tween deck 
plating and upper deck stringers were lighter than would now be 
considered admissible. On examination, a plate at the gunwale, in 
the paddle-box space, was found to have been torn through the solid 
not at rivet holes, and it was judged that the extreme strain to have 
done this, very approximately, must have been about 20 tons per 
square inch. This definite fact, coupled with the reasonable and 
very approximate assumptions of the neutral axis being at the height 
of the centre of gravity of the strained metal of the section; that the 
extension, at any point of the section, would be proportional to the 
distance from the neutral axis; and, lastly, by Hooke's law, ^^ul 
tensio stc w " (as the extension so the force), we were furnished with 
the principles necessary to calculate the amount of strength of the 
section (mathematically strictly proportional to its momeni ofin&riia), 
and we were then able to compare it with the breaking moment, 
taken as some fraction of the product of the length and displacement 
of the vessel ; and, also, see the definite effect due to any other 
distribution or modification of metal in the section. On the direc- 
tion of the late Mr James B. Napier, he (Mr Mansel) investigated 
these matters very fully, and the inaugural paper of the Association 
of Shipbuilders in Scotland, October, 1860, contained the results of 
the application of these principles to a number of cases. Mr Napier 
was a gentleman who took the greatest interest in scientific ques- 
tions, and followed them up with unwearied industry ; and, since it 
appeared that the plating showed started butts, where from the 



2iS On the BuU FaOmings 

distance from the nentral axis the strains must have been veiy mud: 
less than at the gunwale, Mr Napier had full-sized models of doahk 
riveted butts prepared and tested; when, to their surprise, it tamed 
out, with plates one inch in thickness or slightly over, these butts 
were started and practically ruined with a strain of about 8 tons per 
square inch of section; and, consequently, compared with the Uunner 
topside plating, these thick plates did not give nearly the efficiency 
due to their metal, owing to want of strength in the butt fastenings. 
He thought this showed the necessity of double strapping, whic'n 
had been experimentally proved to give a very great increase to the 
tensile strength of the butt. He might have other remarks to make 
upon the paper after he had read it carefiiUy. 

Mr Hknkt Dyer thought there was no question that as a mere 
matter of strength outside butt straps would be effective, but ht 
would like to know whether they would not affect injuriously the 
speed of the vessel? Would the vessel's resistance in passing through 
the water not be greatly increased, not only by the butt straps 
but also by its bottom being more liable to become foul on account 
of the difficulty of cleaning at the ends of the straps ) He was willing 
to admit the superiority of the plan suggested in the paper, so far 
as strength was concerned, but whether the objections to its adoptioD 
in practice would not be insuperable, was another question. 

Mr Mansel said no doubt Mr Dyer had put his finger on the 
objection to butt straps on the outside of vessels. No doubt the 
edges of these plates would very considerably increase the resistance 
of the ship in the water ; but he thought that something might be 
done in the direction indicated in the paper. 

Mr George Russell referred to the small percentage of breaking 
strain at which slip commenced mentioned in the paper, and asked 
if there was authority for it? 

Mr Taylor said that Professor Kennedy, at a meeting of the 
Institution of Mechanical Engineers, giving the result of some ex- 
periments he had made, stated that by the aid of a magnifying glass 
the slip could be seen to begin at about ten per cent, of the breaking 
strength of the joint, while, however, it was not visible to the naked 



of Iron Fessdi. ' 249 

eye till it reached about 25 per cent., or a quarter of the load, for 
the shearing of ordinary rivets. With regard to what Mr Dyer had 
said as to the resistance of outside straps, he might say that there 
was nothing known as to what that might be, with a vessel clean ; 
but if they considered one with a good crop of barnacles on, it 
could not much matter whether the straps were fitted outside or 
not Whether it would be worth while to sacrifice the speed that 
would be lost by outside straps was a moot point. 

Mr SUSSELL asked if Mr Taylor had given any attention to the 
form of butt straps and arrangement of rivets to obtain the maximum 
tensional strength ? Such a mode he had advocated 23 years ago. 
It is illustrated in Plate X. of Volume IX. of the Transactions of 
this Institution. 

Mr Taylor did not think that that would be practicable in ship- 
building where they were confined by the spacing of the frames for 
the width of the butt straps. 

The President suggested the desirability of making an experi- 
ment by adding butt straps to a vessel already built, to find what 
effect they would have on its speed. He proposed a vote of thanks 
to Mr Taylor for his very interesting and practical communication. 

In the discussion of this paper, on the 28th April, 1885, 
Mr W. T. C-DuTTON congratulated Mr Taylor, as a former col- 
league of his own on the staff of the Liverpool Begistry, on the 
valuable paper he had brought before the Institution. The subject 
was one of the greatest importance, and would always awaken the 
interest of shipbuilders. There were one or two points that he 
would like specially to draw attention to. First with reference to 
the shearing strength of the rivets, it was well to notice the differ- 
ence which Mr Taylor showed by his experiments between rivets 
closed by hydraulic pressure and those put in by hand. Mr Taylor 
in accounting for this difference, which appeared to be about nine or 
ten per cent, in fcivour of the former, said (see p. 237), "This is no 
doubt due to increased friction and to the holes being better filled 
by the greater pressure brought to bear upon the rivet, which tends 

8d 



250 OntheBuU Fastenings 

to prove the great superiority of power riveting over hand woik 

It must also have been due to some varying in the effeetiveneBs of 

the riveted work which caused the proportion of load at whidi slip 

occurred to be so irregular." There was no doubt much truth in this. 

but it appeared to him (Mr Dutton) that another cause mig^t be 

looked for, which was that while in hydraulic riveting, the riveta, pro- 

perly heated, were closed at once and done with ; in hand work thcj 

were knocked down through all the stages from hot to cold, and the 

material would suffer to some extent in consequence. Their chief 

surveyor, Mr West, had given considerable attention to the queatioo 

of riveting, and had read an interesting paper on the subject at last 

year's meeting of the Institution of Naval Architects, advocating 

increased fastening and the use of double straps, and if Mr Tayha 

would refer to the existing Rules of the Registry, he would find that 

both quadruple riveting, and double-strapping were provided for. 

As an instance of the former he might mention the case of the 

^^ Manora/' a steel steamer of about 5,000 tons, built two years ago 

by Messrs Wm. Denny Si Bros., in which all the alternate atrakes 

of plating were quadruple riveted, and this vessel continued to do 

her work very satisfactorily. He did not find so much difficulty in 

fitting these wide straps as Mr Taylor anticipated They could be 

checked out or thinned in way of the plating flange of the frame, so 

as to be fitted over it if required, or under it to take the place of the 

liner, and by that means full advantage of the 24»inch space could 

be taken. The fitting of outside butt straps was objected to on the 

score of appearance, and of the resistance offered to speed, but he 

considered both of these objections rather sentimental When they 

found that the large steamer ^^ America," built by Messrs Jaa. and 

Greo. Thomson, and in the front rank of first^^lass passenger traflic, 

had these straps fitted on her sheer strake — ^not light straps such as 

Mr Taylor refers to, but of a very substantial character, and that 

another steel vessel the '^ Manaos," built by the same firm, and also 

engaged in passenger traffic, was similarly fitted he could not think 

that any importance could attach to the question of appearance. 

Then as regarded the resistance to speed, there was not much more 



oflrcn Vessels. 261 

in that^ for although there was very little data to go upon, he could 
say that in cases where these straps of seven and eight-sixteenths in 
thickness had been fitted, there was actually no appreciable differ- 
ence in the speed, and he looked forward to the time when double 
straps would be generally adopted. 

Mr Henry H. West, through the Secretary, said^I have read Mr 
Taylor's paper with very great interest, and I congratulate the Insti- 
tution on having upon its records so thoughtful and practical a paper 
on such an important subject. I very cordially agree with Mr 
Taylor in his conclusion, that butt riveting in relation to the 
sectional area of the plates connected, ought to be considerably 
increased from present practice; but this conclusion immediately 
raises the question, ^* How much ought it to be increased beyond 
present practiced" The answer to this question, in the present state 
of our knowledge, is not easily given. In most engineering 
structures it is customary to apportion the riveting in a joint, so 
that the ultimate shearing resistance of the rivets, shall be approxi- 
mately equal to the ultimate tearing resistance of the plate, at the 
line of probable fracture. This arrangement, I gather, Mr Taylor 
would adopt for ship work, and I freely admit that it would be a 
very great improvement upon present practice; but I venture to 
think that if we are to gain the full advantage of all the material we 
put into our large steamers, there are parts where even this allow- 
ance of rivet power must be exceeded. It is manifest that in such 
a structure as a ship, any slipping in a riveted joint throws an 
undue load on the adjoining material ; and I think anyone who 
gives consideration to the reciprocating nature of the strains to 
which a large steamer is subjected when labouring in a sea way, the 
complexity of the twisting and racking strains she undergoes, and 
the violence of the blows she receives from the sea, simultaneously 
with the constant vibration of powerful machinery, must admit that 
these are conditions which will be favourable to the development of 
slip in even the best riveted joints. There is direct evidence that 
this frequently occurs. In a paper I read on this subject last year 
at the Institution of Naval Architects; and to which Mr Taylor has 



252 On the BuU FadmUnffioflran Vessels. 

done me the honour to refer, I qaoted a number of such instaQces, 
and the list could easily be extended. For my own part» I hold that 
the true measure of the strength of a riveted joint in the moit 
severely strained parts of a ship ia the resistance of that joint to 
slipping. Not simply its resistance to slipping under a continuousij 
and steadily applied strain, but under strains analogous to those to 
which I have referred. Until we know approximately what that 
resistance is, it is impossible to say, with any approach to accuracy, 
how much our butt riveting ought to be increased. For a number 
of years the conviction has been growing upon me that our ship 
riveting arrangements are defective, and whatever may be the pro- 
portions which may ultimately be found to be the right and best 
proportions, we shall in the meantime be making a step in the right 
direction if we very materially increase the rivet power in the joints 
of the most severely strained parts of our large steamers. I hope 
that now Mr Taylor is engaged in practical ship construction, he 
will have the courage of his opinions, and carry out in an acta&l 
case the conclusions at which he has arrived. 



On American RaUtoay Frright Cars, 
By Mr Alexander Findlay. 



(SEE PLATES XX. AND XXI.) 



Received and held as read 28th April, 1886. 



In reviewing the history of the past half-century it doubtless will be 
admitted that nowhere in the world has there been such an enor- 
mous stride in social and material progress and prosperity as in the 
United States of America ; and one of the prime factors — if not the 
most important — has been the development of railways. 

Fifty years ago there was only a few miles — less than one hundred 
— ^running from Boston to Worcester in Massachusetts. Now there 
is over one hundred thousand miles running into every State, and 
opening up and peopling stretches of country which before were 
little else than a wilderness, and running through vast regions, from 
the 3000 miles stretches across the Continent to the overhead line 
round New York, all telling a tale of enterprise and progress. 

Our purpose to-night, however, is not to enter into a history of 
railroad enterprise in the States, for who does not know about the 
great land grants given to railway contractors, or the colossal for 
tunes that have been made or lost in constructing, working, or 
speculating in those roads, of which the Vanderbilts, Fisks, Goulds, 
and others, were and are the leading lights among the '' bulls '' and 
" bears " of Wall Street ? 

Nor is our purpose to consider the construction, and many gauges 
of their roads, through flat prairies or over the Rocky Mountains, 
with their flat-bottomed rails spiked direct to the sleepers, nor their 



254 On Ameriean Bailtoay Freight Cars. 

light tresUe bridges, and viaducts, which will yet be a sonice of 
ever-increasing trouble to their railway engineers. 

Nor is our purpose to deal with their locomotives, which show 
some good and some bad points, compared with our own. Nor thdr 
Pullman, Palace, Dining, Sleeping, or Ordinary Passenger Cars, a 
number of the former of which having been introduced here, hjtve 
added much to the comfort of a long journey, when the purse admits 
of such a luxury ; nor need their excellent ticket or care of lavage 
system detain us, fraught as these items are with so much comfort 
to the traveller compared with our own systems. All the foregoing 
might doubtless prove of general interest, but not quite suitable for 
this meeting, and with the short time at our disposal, we must con- 
tent ourselves with considering freight cars and their construction. 

Under freight cars, however, there are innumerable types and 
modifications for various requirements, such as grain cars, coal cars, 
ore cars, oil cars, timber cars, cattle cars (some of which are faceti- 
ously styled '^palace cars"), refrigerator cars, dump cars, and many 
others, but as a general type we shall consider the grain and coal car 
commonly in use, though each railway may have some modification 
or variation. 

I have chosen this subject, having had several years practical 
experience of this class of car-building with the Missouri Car and 
Foundry Company of St. Louis ; and may say that I have had my 
own knowledge checked up to date, through the kindness of the 
president and superintendent of that company. 

In the general construction of the class of car under consideration 
there has been little alteration for the past fifteen years, except the 
length increased firom 28 feet to 33 feet, and the scantlings somewhat 
heavier, and we shall now proceed to dissect one of those standard 
cars for grain and general merchandise. About five feet from each 
end of the car floor framework there is a cross transom, at centre of 
which an 1| inch diameter pin passes down, and forms the pivot for 
four-wheeled trucks, which, with their short-wheel base, enable those 
long cars to pass easily round very sharp curves, the wheel base 
seldom exceeding five feet. There are many forms and modifications 



On Ammcwn tUMway FreigU Cars. 255 

of those tracks, and the patents for wheels, azleboxes, drawbars, 
brake-gear, &c., are l^on, but we shall take what seems to be the 
most general type in ose, and consider, first — 

Wheels. — With us, as you know, the wheels are usually 36 inches 
diameter, with cast-iron centres or hubs, wrought-iron arms and 
ring, and steel tyre, the hub being bored out, and key-seated for 
keying on to axle. 

The almost universal wheel for freight-cars in the States is of 
cast-iron, and chilled on tread and flange. The most common form, 
and that which seems to give best results, is a double web wheel, 
as shown. Those wheels are cast from a special mixture of metal 
and whilst hot are lifted out of the chills or ring in which they 
have been cast, and placed in air-tight pits for two or three days to 
anneal and toughen. 

The wheels are then bored out on a specially-constructed boring 
mill, the wheel being placed on a table which revolves, whilst a 
vertical boring bar, with roughing tool and finishing tool closely 
following, works quickly down, so that one man can do over seventy 
wheels in 9^ hours. The wheels are not keyed on axles, but 
simply pressed on to the gauge by hydraulic pressure of about 
fifty tons. 

Those wheels weigh firom 500 lbs. to 600 lbs. each, give good 
results, and have frequently been in continuous service for ten and 
even fifteen years. Now that cast-steel is making progress, one 
might think some such wheel could be introduced here with 
advantage, if cast-iron is looked upon with suspicion. 

Asdes. — The axles are usually forged from the best scrap, and 
weigh about d75lbs., and are subjected to severe tests before leaving 
the forge to make sure that all is sound. The standard size for 4 feet 
8| inch gauge road, as adopted by the Master Car Builders' Associa- 
tion, is 6 feet 11^ inches long over all, 4| inches diameter at wheel- 
seat, and 4 inches diameter at centre of length ; and with journals 
7 inches long by d| inches diameter. Those axles are turned on 
special double-end lathe, which enables one man to do 20 axles in 
9^ hours. The wheel-seat only gets roughing cut, and is made 



256 On Ameriem Railway Freighi Cars. 

slightly larger in diameter than bore of wheel, and, as already stated, 
the wheels are pressed on into position by hydraolic preasnrey and 
are not keyed on. 

Journal Bearings, — ^There are many forms and patents in connectioB 
with the aile boxes and bearings, bat probably the best results for 
bearings are obtained from a mixture 7 of best copper to 1 of tin; 
although in others the brass is cast hollow and filled with ** BabbiU 
metal ;" others again, in order to secure the ^best results withont 
incurring the expense of much nicety of [fitting, face the bearings 
with about 1-1 6th inch thickness of lead, which readily adjusts 
itself to the journal, and thereby prevents overheating, as is the case 
unless great care is taken in fitting. 

Axle Bores. — The modifications in the arrangement of oil boxes 
have all a family resemblance — all aiming at protecting the front 
and rear more securely, so that the lubricant may give due effect, 
such as the " Hewitt " door, which, as shown, slides into a wedge- 
shaped groove, and whilst making a secure fixture, is easily removed, 
and the rear has a carefully-fitted vulcanite dust guard. The bear- 
ing has a packing or adjustable wedge piece, which enables a more 
perfect bearing to be easily obtained. 

Springs, — ^The desire to produce the best form and arrangement of 
spring has resulted in many kinds of patents and much trouble and 
expense ; but the round steel bar, coiled one coil within the otber, 
has come into very general use, and gives good results for drawbar 
and buffer springs. For bolster and carrying springs the elliptic 
gives satisfaction when made of such proportions as give the desired 
motion, the usual size for a 20 tons car, having five leaves of 
4^ inches by f-inch steel, coupled together, in what are termed 
^' doublets," thus making a spring 24 inches long, 10^ inches wide, 
and about 9 inches high, giving a motion of 2| inches to 2| inches. 
The cost of these, however, exclude them from general use. 

The round and rectangular coiled bars are more conmion, and are 
coiled in every variety, to get a cluster of coils equal to the work 
required. Sometimes twelve single coils of f inch bar — ^in some 
cases with rubber centre— are grouped in one case, and four of these 



Oh American RaUwajf Freight Cars, 257 

are used to a car ; or other groups will be made thus :-^An outside 
coil 5^ inches or 6 inches diameter of 1 inch or 1^ inch round bar, 
having an inner coil of f inch or f inch bar, and those set in cast 
cases, top and bottom. 

Another much used is composed of a single colli made from 
a rectangular bar 2 inches by 1} inches, coiled to a diameter 
of 9 inches, and a height of 5^ inches; outside of this are 
placed two coils— one on either side — made from a bar f inch by 
I inch, and coiled to a diameter of 4^ inches, and a height of 
G inches (or ^ inch higher than large coil), the three are set in cast 
or malleable cases, the difference in height being made to carry the 
light or empty car without the assistance of the large central coil, 
and gives a very satisfactory motion. 

Trucks. — ^The trucks or bogies on which the^ car body rests has 
been a problem much discussed in trying to decide the best form, 
and this is still far from a final settlement. There are two kinds 
principally in use — one known as the rigid or *' Cleveland " truck, 
and the other the ** swing motion" truck. The Cleveland has some 
good points, and after many years' experience has been preferred for 
its simplicity of construction and non liability to get out of order. 
This truck is constructed of a top and bottom bolster (or spring 
plank and bolster), the top plank being usually 13 inches by 8 
inches trussed, with 2 | inch rods, as the half weight of car comes on 
centre plates screwed to centre of this timber, the bottom or spring 
plank is 13 inches by 5 inches, connected to the axle boxes by two 
arch bars of 3 inches by 1 inch iron and 3 inches by i inch tiebar, 
which are secured to the timbers by cast-iron columns and guides, 
the cases with group of coil springs being placed between said 
timbers. 

The swing motion truck is of somewhat similar construction 

to the foregoing, so far as the arch and tiebars are concerned, but 

the spring plank and bolster are hung by links and pins from the 

upper edge of two 13 inch by 5 inch timbers set on edge, and having 

a distance casting placed at each end between these timbers, and 

well secured to them. The swing motion is on account of the bolster 

34 



258 On American Railway Freight Can, 

and spring planks hanging, with a little spare room between these 
two vertical timbers, and altogether make a track more adapted to 
tooghly constructed or poorly ballasted roads, and is much easier on 
the body of car as well as on journals and bearings, owing to the 
swing motion accommodating itself to inequalities and irr^^lar 
strains. The greater number of pieces, the difficulty of easy inapeo- 
tion, the expense of renewal and increased first cost, are some objec- 
tions to this truck. 

Timber has been mentioned as the constructive material, and 
because it is so plentiful; but now, instead of the two timbers 
enclosing the swing beam, there is an extensive use of iron channel 
bars, 10} inches by 8 inches, and iron is gradually working into oae 
for other parts as well 

A feature lately introduced iu heavy cars for cairying ore or 
stone, has been to apply a third track to the car — that is, plac- 
ing a truck under the centre of the car. To do this the car 
has X ^^ ^^ secured to the sills crosswise, and rollers on 
suitable axles are placed on the truck, and arranged to allow a 
lateral motion when going round curves. These are said to ^ve 
good results where a continuous service in one locality is found 
practicable, otherwise one would assume that a shorter car, capable 
of being safely carried by two trucks, would be much preferable. 

Body of Car. — The body of car is usually 33 feet long by 9 feet 
wide — a very great departure, indeed, from our short cars or tracks, 
as we call them ; and for coal cars have shallow sides about 18 inches 
to 24 inches deep, and for grain and other traffic have side framing 
about 7 feet high, with roof over all. 

The trausoms or body bolsters on which the trucks pivot, are now 
often made of 7-iiu by J-iu. iron, although oak transoms 13 in. by 5 in , 
trussed by two l-in. rods through and over the sills are still much used. 
The main or floor framing consists of six longitudinal timbers and 
two end timbers, with two intermediate timbers across under sills tor 
trussing longitudinals ; also the two transom timbers about 6 feet 
from ends. The timber used is mostly pine, although the two 
centre longitudinals to which the draw timbers ai*e secured are oak. 



On American Railway Freight Can. 259 

Ei^t inches by 4^ inches is the scantling nsed for this framing, and 
those are well tenoned and secured by bolts and plates to each 
other, and have four longitudinal truss rods I inch or 1^ inch diam- 
eter running through end timbers, over transoms and under the 
intermediate truss timbers, thus stiffening framework. 

Drawbars, — ^Of all the questions in car construction, this is mean- 
while the most perplexing, the drawbar acting both as coupler and 
buffer in most of the freight cars. There are several thousand 
patent couplers, many being automatic and having good points, 
and all desirous of having their patents introduced. This important 
matter is now being made a subject for legislation, and several are 
being tested and a general discussion is being carried on amongst 
railway managers, car builders and others, which must result in 
ultimate good. A very common drawbar is that with single coupling, 
link and pin in cast iron drawbar, secured by draw and buffing plates 
with volute spring to relieve the shock when starting or stopping 
car. A similar drawbar is arranged to receive three coupling 
links, so that in the event of a breakdown owing to a link giving 
way, another can at once be available. There are also ^' continuous '' 
drawbars which give good results provided every part is reliable, 
which is not always the case. One with some points of excellence 
consists of an abutting plate 7 inches by li inches, let into the draft 
timbers, and secured by two bolts running across close behind it. 
The volute spring is placed between this plate and the end of the 
cast-iron drawbar. A tail pin passing through both, and with 
cottar in the end outside the plate, but which is not brought into 
service unless some other part fails. A wrought-iron bar 24 inches 
long, 5 inches by 1 inch, passes through drawbar, and projects 
beyond both draft timbers, with room to move longitudinally in the 
timber equal to the motion of the spring, those slots in the timber 
are protected by comer irons, and when drawing or buffing, this 5 
inches by 1 inch bar should act about the time the spring motion is 
exhausted. There is also two 1^ diameter rods having a loop on 
each end that fits over those 5 inches by 1 inch bars, and thus form 
a continuous pull on rear end of car. Should these rods give way, 



260 On Amerkan BaUway Fr^gki Cart. 

then the 5 inches by I inch bars {Musing through the draft timbers 
will act and the drawbars still be in operation, and if these give 
way, the tail pin will continue to do service. The weak point, 
however, is the cast-iron drawbar, which has too long held ic§ 
position, but is now giving place to drawbars made of malleable 
iron. 

We will now pass to the body framing, which in coal cars consisb 
of short wooden posts set vertically in cast-iron sockets, and to which 
the timber forming sides and ends is secured. 

Grain and covered cars have, however, comer and intermediate 
posts about 7 feet high, and bracings A\ by 2i in., pine being osnal, 
and so framed and secured by iron plates and rods as to make a 
strong framing, which is lined outside by | inch boarding, and inside 
up 3 feet to 4 feet for grain. The doors for those cars nsuaUy slide 
outside on an iron rail, and there are many patent fixtures arranged 
for holding door close to body of car so as to prevent sparks from 
getting in. There is also an inner door 3 feet to 4 feet high to 
prevent the grain from pressing against the outer door, or from 
leaking out, and some most ingenious devices have been patented for 
easy fixing and removal of those doors when not in use. Roofs for 
those grain and covered cars are usually made with about one foot 
of rise at centre, and are often made up of cross raften> about 2 feet 
apart, and with longitudinal purlins, on which two thicknesses of 
I inch lining, having feather and grooved joints, are fixed and all 
well painted and watertight. 

Galvanised iron sheeting. No. 24 B.\V.G., is, however, being 
extensively used for roof covering, and does good service. A 
very important equipment of a car is an efficient brake, and 
the usual practice for freight cars is to apply a brake shoe to 
each wheel, those being acted on by rods and levers attached to 
I inch chain which simply winds round a vertical rod having 
hand wheel and pawl attachment. Some of the best roads are now 
equipping their entire freight stock with good automatic brakes, 
notably the '^ Westinghouse,'' which seems to take and keep 
the lead for efficiency in such appliances. The American Brake 



On Ammcan Bailivay Freight Cars, 261 

C07. of St Louis have, however, a goodly number of their brakes in 
use, which device is operated only by the pressure of the drawbar, 
which, upon a stoppage or sadden reversal of the engine sets all the 
brakes instantly in action. There is one great advantage, viz., that 
there is no connection between the cars, and any car may be operated 
on independently in any part of the train, which is not the case in 
the Westinghouse, as it is connected with the engine, and operated 
by the engineer. We must not, however, overlook the fact that 
where a train breaks in two from any cause, then the Westinghouse 
at once operates on every brake automatically. 

And now, to sum up, it may be asked. Why do they not build their 
cars of iron, and with the superior fittings such as are common on the 
Indian State and similar railway waggons 1 To which we reply that 
timber being cheap and plentiful, and the car works furnished with 
excellent wood-working machinery for planing, tenoning, morticing, 
boring, &c., such cars can be turned out very quickly, and above 
all cheaply —which is a great desideratum with many of the Railway 
Companies— compared with anything that could be made in iron. 
Such works as the Missouri Car and Foundry Coy. turn out as many 
as twelve fully equipped cars, of the kind we have been considering, 
foch day, casting their own wheels and doing their own smith work. 

In addition to some of the railway companies that build their own 
cars, thjre are many private companies engaged in the car building 
business, and which turn out the enormous requirements for the 
multitude of railways throughout the country. 

And now, is there anything to learn from those long American Rail- 
way Freight Cars ? probably they are more the special design required 
for such long journeys as many of them require to take continuously. 
Still, could there not be such a truck as the '* Cleveland " introduced 
under say our long six-wheeled rail waggons with advantage, for at 
present it is impossible to get round the curves in many of our 
workshop yards with such waggons ; even the 16 feet and 18 feet 
waggons with 9 feet wheel base do not take the curves so com- 
fortably as the long American cars. Certainly, those long cars do 
strike a stranger as something very different from our short dumpy 



2G2 On American BaUway Freight Cars. 

waggons— or tracks as we term them-r-and the chilled wheeb and 
pivotting trucks do suggest some possible improyements such as are 
hinted above. In conclusion, it is hoped, that this paper although 
somewhat hurriedly written, may not be altogether uninteresting 
to some of our members engaged in rolling stock constructiony and 
may stir them up to favour us with a paper shortly, on home 
practice^specialties. 



On Sinking the Cylinders of the Tay Bridge by Pontoons. 
By Mr Andrew S. fiiooABT. 



(SEE PLATES XXII., XXIII., AND XXIV.) 



Received £4th February^ and held as read 28th Aprils 1886, 



One of the most common forms of foundations now adopted, on 
which to build the superstructure of a modern bridge is the cylinder. 
But, as the foundations are often in positions difficult to get at, and 
when there, to remain at, owing to causes such as the rise and fall 
of the tide, rapidity of the current, storms, &c., a difficult problem 
in connection with the building is often. How are the cylinders to 
besunkf 

One of the easiest, and at the same time most sure methods now 
in vogue, is to build a wooden stage around the place where each 
cylinder is to be sunk, and from this as a working platform, lower, 
dig out, concrete, and carry them up to the desired height. 

Some cylinders are of sufficient capacity to float themselves with 
^ierfect safety to their respective positions, as well as be made carry 
all the sinking apparatus and platform necessary to regulate their 
descent into their final resting place. Or again, if we drop to the 
smallest form of cylinder, we would instance the screw and the 
hollow pile, the former of which is sent home by the simple, though 
sometimes difficult process of screwing into the ground, while the 
latter is driven. 

While work can, and is being done every day, by methods similar 
to these, it is readily understood that much is done (especially if a 
stage has been constructed) which requires to be undone with a con- 
sequent loss of time and money. To use the old method of staging, 



264 On Sinking the Cylinders 

for such a work as the New Tay Viaduct would have require abnost 
a forest of timber, for this aloue, and owing to the great depth ot 
water, the work would have been both tedious and expensive. 

Before proceeding to sketch the novel method which has, however, 
been adopted, let us look at the primary conditions which must 
necessarily be fulfilled by whatever form of platform is used. 

Ist, — There must be a working platform, on which can be placed 

cranes and other machinery. 
2nd, — The platform must be high enough to permit of work 
being conducted from and upon it at all states of the tide. 
3rd, — It should abo be capable of being removed speedily from 
one position to another. 

These primary conditions, enhanced by many other advantages, 
are practically realised in the pontoons designed by Mr Arrol, and 
now used successfully by him in sinking the cylinders of the New 
Tay Viaduct. The pontoons used (of which there are four) are all 
made up of tanks, for the sake of convenience, which are rigidly 
fastened together in the form of a rectangle ; and they vary in size 
from 56 feet by 36 feet 6 inches, by 6 feet deep, as in the smaUest, 
to 81 feet by 66 feet, by 7 feet deep, as in that of the largest 

We propose to confine our description to one of these, as all are 
the same in principle, varying only in some of the details. 

Fig. 1, Plate XXIL, presents a plan of No. 2 pontoon. You will 
observe there are two main tanks running the whole length of Uie 
platform, connected together by one small tank, and several main 
cross girders, the full depth of the tanks, as well as, top and bottom 
outer cross girders. In both of the main tanks there are two 
rectangular openings, one at each end. Through these the legs are 
passed, which are used for raising and lowering the piatform. To 
the tanks are fixed at these openings steel plates for carrying the 
hydraulic cylinders required to perform this action. 

Equally from the centre, and at the distance of 26 feet, centra to 
centre, the large cylinders are lowered (one at a time) through the- 
centre openings in the platform, and this too by special hydraulic 
machinery, being guided in their descent by the vertical guides 6 



of the Tay Bridge by Pontoons. 265 

which in their turn are attached to the cross girders H H^ fixed at 
the top and bottom of the tanks. The cross girders are only tem- 
porarily fastened, so that in the event of the platform being raised 
somewhat out of position, they can be shifted, and with them the 
guides, thus making it practicable with almost a minimum of labour 
to lower the cylinders in their true position, even although the 
pontoon has been pitched slightly out of place. On one of the main 
tanks there is fixed a crane which is used for lifting material on to 
the platform, and also for excavating by means of mechanical 
diggers, the sand and earth within the cylinders. In the small con- 
necting tank is placed a boiler and engine, used for driving the 
hydraulic pumps, working windlass, &c., as may be required. Other 
machinery and gear, such as portable boiler and engine, centrifugal 
pumps, capstans, bollards, fairleads, workshops for the men, all find 
a place on this sometimes floating staging, at other times stationary 
and high out of the water. 

Before this description can be of much practical value it will be 
necessary to describe more in detail the principal parts of the 
pontoon, and the mode by which it is wrought. The method of 
raising and lowering the platform is shown by Fig, 3, Plate XXIII. 
A is one of the legs, which is 5 feet in diameter, and of a conical 
shape at the bottom, to prevent the ground on which it rests being 
scoured from underneath. On it is fixed four heavy steel plates 
B B, two on each side, about 16 inches apart^ having holes G G 
passing through them, spaced about 6 inches apart. Sliding within 
these two plates, but fixed to the platform, are other two D D, 
having holes the same size and pitch as in the outside plates, and 
carrying between them a hydraulic cylinder E, provided with a 
piston P, piston rod R, and crosshead I. The action is as foUows ; 
suppose the piston P to be at the top of the cylinder through the 
crosshead I, and outer plates B B, a steel pin is passed, when water 
is admitted the cylinder £ is forced up, because the outer plates 
B B on which the pin rests are fixed to the leg A which in its turn 
bears on the ground. The plates D D are thus lifted, and with them 

the platform. When the cylinder has been raised about six inches, 

35 



266 On Sinking the Cylinders 

the holes through the inner plates D D and cater plates B B are b 
line. Into one of these is now passed another steel pin. If the 
water in the cylinder E is allowed to go free, the platform will aov 
hang on the pin jost inserted, and allow the first to be withdrawn. 
The piston is now forced to the top of the cylinder, and the first pin 
being again inserted, all is ready for another lift. From this you 
can readily perceive the only limit to the height to which the plat- 
form may be raised is the length of the leg and its accompanying 
plates. In lowering the platform this action is simply reversed. 
Both cylinders at each leg are wrought at the same time, and, if 
convenient, the others at the remaining comers of the platform. 

The large foundation cylinders, two of which are in each pier 
are lowered into position by the hydraulic apparatus shown by 
Figs. 1, 3, and 4. Each of these cylinders including au inside 
brick ring, which must be built before being lowered into posi 
tion, weighs about 50 tons, varjring less or more according Uj 
the depth to which it is to be sunk. The hydraulic cylinder 
and links for lowering these foundation cylinders are shown by 
Fig. 4, Plate XXIV. Figs. 1, 3, and 4, show the manner in which 
these are wrought C is the cylinder to be lowered. A the hy- 
draulic lowering cylinder. P the piston and hollow-trunk, through 
which is passed the steel links L, these being single and double 
every alternate length, and through all are cottar-holes about 10 
inches apart. B is a bow, fixed on to, and over the hydraulic 
cylinder A, through it the links are also passed, they being in short 
lengths and attached to one another by means of bolts. At the bottom 
of the cylinder C, these links are firmly fixed to a plate which in its 
turn is securely bolted to the cyb'nder. The action in lowering is as 
follows : — Suppose the combined piston and trunk P is almost raised 
to the top of its stroke, by admitting water through a cock at Q, a 
cottar is able to be inserted through the hole H, Upon water beini; 
again admitted, the links are raised and with them the cylinder C. 
thus relieving the top cottar (presently resting on the bow), which is 
then withdrawn and inserted in the first hole higher up. The waWr 
being now allowed to escape, the piston P and links L, with the 



0/ the Tay Bridge by PonUxm. 267 

large cylinder C attached, descend till the top cottar again rests on 
the bow B. The lower cottar is then free to be withdrawn and 
inserted in the first hole higher up, and this done we are ready to 
begin a new stroke, and so continuing the cylinder C is gradually 
lowered till it reaches the river bed. Four of these hydraulic 
cylinders are employed in lowering one foundation cylinder. 

The water for all the hydraulic machinery is obtained from the 
pumps ahready mentioned. 

The diggers used are of various types, but principally consist of 
those with hinged automatic doors, which are open when the digger 
is dropped into the ground, and closed by links in the act of with- 
drawal. These are used principally in excavating the sand and 
other soft materials, others having hydraulic cylinders for opening 
and closing strong toothed doors, in order to tear and bring away 
the softer rocks and hard clays, have been used, but to no extent. 
In some cases a centrifugal pump has been utilized to great advan- 
tage for taking out the silty sand within the cylinders. The main 
suction pipe has two inlets, to each of which is attached a flexible 
rubber pipe. While the nozzle of the one inlet is being held to 
the sand by a diver, the other is loose and sucking in clean water. 
By using this precaution the pump seldom gets choked, and with 
some kinds of deposit this method is found to give excellent results. 

After this preliminary description you will readily follow the 
mode of working the pontoon during the sinking of a pier. The 
first thing necessary to be done is to float out the pontoon as nearly 
as possible to its true position, immediately over where the cylinders 
are to be sunk. It is taken to its place by means of the crane 
already on it, acting as a windlass, the. ropes and chains being 
fastened to buoys and the piers of the old bridge. Placed in posi- 
tion it is only the work of a few minutes to drive away the tem- 
porary supports on which the legs are resting (the pins at this time 
being all removed) when they gradually sink to the bottom. The 
hydraulic apparatus used in raising the platform (already de- 
scribed and shown in Fig. 2, Plate XXII.) is now brought into 
requisition, and made to lift it to the desired height. This is 



268 On Sinking the Cylinders 

generally attained when the bottom of the pontoon is about two 
feet under high water level. The best, and occasionally the onlj 
time the pontoon can be brought into position, before being raised, 
is at high tide. It is the best because the platform is about as high 
as it requires to be, and occasionally it is the only time, on aoconnt 
of the depth of water required to float it in. Anchors and 
chains are now called into requisition to assist the legs in keeping 
the platform steady, which, by the way, is found to be remarkably 
so, even in the roughest weather. When standing on the platform, 
during a high wind, and carefully watching the movement at high 
tide, when the waves art dashing against it, the oscillation is found 
to be very slight, even with both these adverse circumstances to its 
steadiness in play. 

All done we have a fixed platform, above the influence of the 
tide, and at the same time in the best attainable position relative to 
the pier at which work is about to be commenced. 

Upon the platform is also placed all the necessary apparatus for 
the lowering, sinking, and building of the cylinders (material of 
course excepted). 

The cylinders are now built over one of the central openings of 
the platform, being brought in complete rings, for convenience in 
handling, as part of the fixing together has to be done while they 
are thus being built in position. As section after section of iron is 
added (within), on the inner side, is built a ring of brick in cement, 
thereby increasing the weight, which assists during the process of 
digging to sink the cylinder and also keep it in form, as well as 
fulfilling the primary object of its being there, namely, to insure the 
safety of the structure in the eveot of the iron being corroded away. 
While the rings are in course of being added, all at the same time 
is lowered by the hydraulic apparatus already described till the 
cylinder reaches the river bed. The digger is now set to work 
and gradually excavates the material from within the cylinder, and 
thereby makes a way for it to settle down into the ground, and this 
is continued until it reaches its proper depth, 
Although^apparently easy and simple on paper the diflBcultios in 



of ike Tay Bridge by Pontoons. 269 

the way pieventing the desired end being attained are sometimes 
enormous ; for example, jou may come on a bed of boulders (this is 
found in many piers, being the protecting rubble of the old bridge 
piers) or even one large one, say one quarter within and the 
remainder outside of the cylinder, or get into clay so hard that the 
di^er can barely cut into it, and yet so leaky as to make it impos- 
sible to pump the cylinder dry. Or there may be difficulties, the 
causes of which if known, could be as easily counteracted and over- 
come, as was the case when the sand saddened within the cylinder 
during the ebbing of the tide, on account of the water being higher 
within than without ; the digger in these circumstances brought up 
only a small quantity at a time, nothing to be compared to what 
was done when the water was kept a little lower within than with- 
out. This is easily accomplished by the artificial means of pumping, 
the effect of which is to cause a little water to be constantly leaking 
through the sand into the cylinder, thereby keeping it loose and 
consequently making it easy to be dug into. 

At other times the diggers &re completely useless for excavating 
the n^aterial within the cylinders; a good alternative (if at all 
possible) in a case of this kind is to force the cylinder down by 
piling on weights till it becomes practicable to pump it dry, after 
which it can be dug out by hand. Before this has been accom- 
plished in some cases it has been necessary to add as much as 400 
tons of artificial loading to some of the 15-feet diameter cylinders. 
If the cylinder cannot be made watertight, then in a case of this 
kind resort has to be had to divers. 

When a cylinder has reached the desired depth, and pro- 
vided the bottom is satisfactory, filling in with concrete is 
commenced and continued till it reaches the top of the iron- 
work. The material for making the concrete, (gravel, and cement) 
is in most cases lowered fiom the old viaduct, which is only 
60 feet to the eastwlard, and runs parallel with the new, except a 
short piece at the ends. The gravel is emptied out of the trucks 
into a shoot resting on the pontoon platform, and is there mixed 
and afterwards thrown or lowered into the cylinders, as the case 



270 On Sinking the Cylinders 

may require. The second cylinder having been placed in poeitioii 
in a similar manner to the first, the platform is now lowered and 9i 
high tide is floated away over the top of the now sank cylinders, 
the tops of which are only visible at extreme low water, thus 
leading the uninitiated to suppose little has been done because little 
is seen. 

Cast-iron weights are now built on girders above the cylinders for 
the purpose of testing the sufficiency of the foundation. Sufficient 
weight is laid on to cause a pressure of five tons per square foot on 
the whole area under the cylinders. If they sink at all these 
weights are allowed to remain until all indications of such are 
stopped, after which they are transferred on to the next set bj 
means of a wire cable or barge. It is here worthy of notice that 
the test load placed on the piers is 33^ per cent in excess of the 
weight that would be brought, although the two lines were fully 
loaded with trains. 

On the removal of the weights temporary caissons are fixed to 
the permanent cylinders by bolts and pumped dry. The remaining 
blue brick, outer shell, concrete, and stone work above low-water is 
then executed. Twenty feet down into this are built the holding- 
down bolts, 16 in number, in each pier, all 2^ inches diameter. 
The caissons are removed and afterwards the connecting piece 
between the cylinders and the remainder of the pier is built up to 
and under pinned beneath the iron base on which the wrought-iron 
superstructure rests. 

Progress is thus going on at several piers at one and the same time. 
1st, — The pontoon, lowering, digging, and concreting. 
2nd, — Testing the value of the foundations. 
3rd, — ^Building under high water, within the temporary caissons. 
4th, — Finishing remainder of pier, to underside of ironwork. 

This again is but the starting point, from which the iron super- 
structure, as shown in Fig. 5, Plate XXIY., begins to rise (in stages 
also) to be followed by the placing of the girders and flooring, on 
which, finally, the track is laid. 

Although the advantages gained by using pontoons, such as those 



of the Tay Bridge by Pontoons. 271 

described are apparent to all, it is at the same time evident, they 
could not be used to advantage, except on works of some magnitude 
where, for instance, there are a goodly number of piers to be put 
down, and also difficulties to be overcome, for grappling which, they 
are peculiarly suited. 

The new Tay Viaduct furnishes such work and difficulties. 

The pontoon on the Dundee side, sunk and concreted, one com- 
plete pier (of two cylinders, 10 feet diameter each) per week, for 
nearly two months on end. The greatest difficulty to contend with 
being the shallowness of the water in which it had to work. The 
depth to which each of these cylinders is sunk varies from about 16 
feet to 26 feet under the bed of the river. 

Such is a very brief resume of the foundation work, and the mode 
by which it is being accomplished, at this Viaduct, at the present 
time. Time alone will tell, when the results are balanced, if the 
decision was altogether wise, which fixed on this novel method of 
carrying out a vast undertaking. 



Institution of Engineers and Shipbuflderg 

i3iT sooTnLi-A-irr) 

(IKCOBPOBATED). 



TWENTY-EIGHTH SESSION, 1864-85. 

MINUTES OF PROCEEDINGS. 



The First General Meeiing of the Twenty-Eighth Session of 
the Institution was held in the Hall of the Institution, 207 Bath 
Street, on Tuesday, the 28th October, 1884, at 8 P.M. 

Professor James Thomson, C.E., LL.D., &c., President, in the Chair. 

The Minute of Annual General Meeting of 22nd April, 1884, was 
read and approved, and signed by the President. 

The President delivered his Inaugural Address. 

On the motion of Mr Kobert Mansel, a hearty vote of thanks 
was accorded the President for his address. 

The Discussions of the following Papers, read at Annual General 
Meeting in April, were proceeded with and terminated, and a vote 
of thanks awarded the Authors : — 

On *'The Properties of Screw Piles," by Mr Wm. Murray, CE. 

On " Fog Signalling as Applied to Lighthouses," by Mr George 
Slight, Jun 

On " Approximation to Curves of Stability from Data for Known 
Ships," by Messrs F. P. PcRVis and B. Kindeumann. 

Members elected at last General Meeting were presented with 
Diploma of Membership. 



274 Minutes of Proceedings. 

The Second General Meeting of the Twenty-Eighth Session 
of the Institution was held in the Hall of the Instltutioii, 207 Bath 
Street, on Tuesday, the 26th November, 1884, at 8 p.m. 

Professor James Thomson, C.E., LL.D., &c , President, in the Chair. 

The Minute of Greneral Meeting of 28th October, 1884, was read 
and approved, and signed by the President. 

A Paper on " Manipulating the Material and Drilling the Great 
Tubes required in the Forth Bridge," by Mr Andrew S. Biggart. 
was read, a discussion followed and was continued till next Genial 
Meeting. 

A Paper on *^ Energy and Entropy and their Applications in ihe 
Theories of Air and Steam," by Mr Henry Dyer, G.K, was read, 
the discussion of which was deferred till next General Meeting. 

The President announced that the Candidates balloted for had 
been elected, the names of these gentlemen being as follows]: — 

AS members : — 
Mr Andrew S. Biggart, Forth Bridge Works, South Queensferry. 
Mr E. Walton Findlay, Ardeer, Stevenston. 
Mr John Wildridge, Consulting Engineer, Sydney. 

AS graduates : — 
Mr Archibald M'Beth, Apprentice Engineer, ill Govan Road. 
Mr Thomas Millar, Ship Draughtsman, 31 Grange Koad, West, 

Jarrow-on-Tyne. 



The Third General Meeting of the Twenty-Eighth Session 
of the Institution was held in the Hall of the Institution, 207 Bath 
Street, on Tuesday, the 23rd December, 1884, at^8 P.M. 

Professor JAMiiS Thomson, C.E., LL.D., &c.. President, in the Chair. 



Afinutis of Fioceedingg. 275 

The Minute of General Meeting of 25th November, 1884, was read 
and approved, and signed by the President. 

Mr Henry Dyer gave notice of the following motion : — " That 
the Council be requested to consider how the Library may be made 
more worthy of the Institution, and to report to an early meeting." 

The discussion of the following Papers was resumed and terminated : 

On ^^ Manipulating the Material and Drilling the Oreat Tubes 
required in the Forth Bridge," by Mr Andrew S. Biggart. 

On " Energy and Entropy and their Applications in the Theories 
of Air and Steam," by Mr Henry Dyer, C.E. 

Votes of thanks were awarded the Authors of these Papers. 

Mr WiLUAM Denny read his Paper on " Mr Mansel's and the 
late Mr Fronde's Methods of Analysing the Results of Progressive 
Speed Trials," a discussion followed, and was continued till next 
General Meeting. 

It was agreed that Mr ManseFs " Letter of Eeclamation," 1884, 
and also Mr Fronde's letter to Mr Mansel, of date 23rd September, 
1876, should be published as forming part of the discussion on this 
paper. 

The reading of the other Papers on " Notice " was deferred till 
another Greneral Meeting. 

The President announced that the Candidates balloted for had 
been elected, the names of these gentlemen being as follows : — 

AS MEMBERS :— 

Mr John W. W. Drysdale, Engineer, 5 Whitehill Gardens. 
Mr Peter N. Cunningham, Engineer, 5 North-east Park Street. 
Mr FiNLAY FiNLAYSON, Mechl. Engineer, Glengamock Steel Works 
Mr John M*Beth, Master Shipwright, 5 Park Street, Kinning Park. 
Mr James M'Lellan, Mechanical Engineer, 10 West Garden Street. 
Mr John M'Neil, Mechanical Engineer, Helen Street, Govan. 
Mr Wm. H. Nisbet, Mechanical Engineer, Mavisbank, Partickhill. 
Mr James Williamson, Shipbuilder, Barclay, Curie, & Co., Limited 

Whiteinch. 



276 Minutes of Proceedings. 

AS AN ASSOCIATE : — 

Mr W. S. C. Blacklky, Iron Merct, Blackley Young & Co., Holm St. 

AS GRADUATES:— 

Mr Arthur G. Auden, App. Engineer, 9 Carmichael Street, Govan. 
Mr D. C. Qlen, Jun., Apprentice Engineer, 14 Annfield Place. 
Mr John Howarth, App. Meckanical Engineer, 37 Bentinck Street 
Mr Robert Logan, Ship Draughtsman, 3 Haybum Cres., ParticL 
Mr Jas. M'Ewen M'Intyre, Engineer Draughtsman, Dalmuir. 
Mr W. J. Marshall, Engineering Draughtsman, 3 Minerva Street. 
Mr R. Mansel, Jun., App. Ship Draughtsman, 4 Clyde View, Pt*k. 
Mr James G. Reid, Jun., App. Ship Draughtsman, 4 Holland Place 
Mr David W. Sturrock, Engineer Draughtsman, 11 Florence Place. 
Mr Wm. TnoBfSON, Engineering Student, 15 Bumbank Gardens. 
Mr John Thomson, Jun., Apprentice Engineer, 15 Bumbank Gardens. 



The Fourth General Meeting of the Twenty-Eighth Session 
of the Institution was held in the Hall of the Institution, 207 Bath 
Street, on Tuesday, the 27th January, 1885, at 8 p.m. 

Professor James Thomson, C.E., LL.D., &c.. President, in the Chair. 

The Minute of General Meeting of 23rd December, 1884, was read 
and approved, and signed by the President. 

In accordance with previous notice of motion, Mr Henry Dyer 
moved as follows: — " That the Council be requested to consider how 
the Library may be made more worthy of the Institution, and to 
report to an early meeting." This was seconded by Mr Jambs 
Lang, and being put to the Meeting was agreed to. 

Mr Charles C. Lindsay proposed the following motion :— 'That 
the sum of £20 or thereby shall be expended annually out of the 
funds of the Institution in the purchase of books for the Library in 



Minutes of Proceedings. 277 

addition to the ordinary expenditure in binding, &c., all such books 
to be chosen from the Becommendation Book and approved by the 
Council." This was seconded by Mr RoBT. Duncan, of Whitefield. 

As it was explained to the Meeting that the Council had already 
adopted this resolution, and that it therefore came before the General 
Meeting under Rule 47 as an alteration of the Bye- Laws, the motion 
was tlien put to the Meeting, and was agreed to. 

The discussion of Mr William Denny's Paper on '* Mr Mansel's 
and the late Mr Fronde's Methods of Analysing the Results of Pro- 
gressive Speed Trials/' was resumed and occupied the rest of the 
evening. On the motion of Mr Henry Dyer the discussion was 
adjourned to next General Meeting. 

The President announced that the Candidates balloted for had 
been elected, the names of these gentlemen being as follows : — 

AS MEMBERS: — 

Mr William Arrol, Mechanical Engineer, 10 Oakley Terrace. 

Mr Peter Fyfe, Mechanical Engineer, 234 Parliamentary Road. 

Mr Charles A. Knight, Engineer, 107 Hope Street. 

Mr James Rowan, Marine Engineer, 231 Elliot Street. 

Mr GEORrsE W. Thode, Mechanical Engineer, 107 Hope Street. 

AS IJRADUATES : — 

Mr Wm. D. Ferguson, Assistant Engineer, 63 Finlay Drive. 
Mr Alex. M. Gordon, Ship Draughtsman, 3 Wallace Grove Place. 
Mr John M*Millan, Engineering Student, 2 6 Ashton Ter., Hillhead. 
Mr James L. Proudfoot, App. Civil Engineer, liU \V. George St. 



2 78 Minutes of Proceedings. 

The Fifth Gensral Meeting of the Twenty-Eighth Session 
of the Institution was held in the Hall of the Institution, 207 Bath 
Street, on Tuesday, the 24th February, 1885, at 8 p.m. 

Professor James Thoicson, C.K, LL.D., &c.. President, in the Chair. 

The Minute of General Meeting of 27th January, 1885, was 
read and approved, and signed by the President. 

The discussion of Mr William Denny's Paper on '' Mr Maiisel's 
and the late Mr Froude's Methods of Analysing the Results of Pro- 
gressive Speed Trials," was resumed and terminated, and a vote of 
thanks awarded Mr Denny for his Paper. 

The discussion of Mr Allan Clark's Paper on ''Electrical 
Navigation/' was deferred till next General Meeting. 

The President announced that the Candidates balloted for had 
been elected, the names of these gentlemen being as follows : — 

AS MEMBERS : — 

Professor Francis Elgar, Naval Architect, 17 University Gardens. 
Mr James Samuel, Jun., Mechanical Engineer, 238 Berkeley Street. 

AS AN associate :— 

Mr lioBERT Darling, Manager, North British Steam Packet Co.. 
5 Summerside Place, Leich. 

AS GRADUATES: — 

Mr Wm. S. Dawson, Engineering Draughtsman, 24 Glen St., Paislej-. 
Mr John Inglis, Ship Draughtsman, Bonnington Brae, Edinburgh. 
Mr John Lang, Draughtsman, 6 Elderslie Street, Anderston. 
Mr John T. Ramage, Apprentice Engineer, The Hawthorn's, 

Bonnington, Edinburgh. 
Mr Charles H, Wannop, Draughtsman, 12 Derby Street. 



Minutes of Proceedings, 279 

The Sixth General Meeting of the Twenty-Eighth Session 
of the Institution was held in the Hall of the Institution, 207 Bath 
Street, on Tuesday, the 24th March, 1885, at 8 p.m. 

Professor James Thomson,;C.E., LL.D., Ac, President, in the Chair. 

The Minute"'of General Meeting of 24th February, 1885, was read 
and approved, and signed by the President. 

The discussion of Mr Allan Clark's Paper on ''Electrical Navi- 
gation," was terminated and a vote of thanks awarded Mr Clark 
for his Paper. 

The following^Papers were read : — 

On j'' A Continuous Regenerative Gas Kiln for Burning Fire-bricks, 
Pottery, &c.," by Mr John Mayer, F.C.S,, and on "The Butt 
Fastenings of Iron Vessels," by Mr Staveley Taylor. 

Discussions followed and were continued to next General Meeting. 

Votes of thanks were awarded the authors of the Papers read. 

Mr 'And. Maclean and Mr David Kinghorn were unanimously 
appointed Auditors of the Annual Financial Accounts. 

The President announced that the Candidates balloted for had 
been elected, the names of these gentlemen being as follows : — 

as members : — 

Mr John B. Cameron, Engineer, 160 Hope Street. 

Mr Edmund Morr, Board of Trade Surveyor, 7 York Street 

Mr Alexander Thomson Orr, Mechanical Engineer, Messrs Hall, 

Russell, & Co., Aberdeen. 
Mr|W. Carlilk Wallace, Mechl. Engineer, Maryland, Dumbarton. 

AS AN ASSOCIATE:— 

Mr James S. Gardner, Engineering Lithographer, 52 North 
Frederick Street. 



280 Minnies of Proceedings. 

A8 GRADUATES: — 

Mr Alexander Bishop, Assistant Engineer, 3 Germiston Street. 
Mr Matthew Rttohie Brown, Engine Draughtsman, 6 Hamilton 

Place, Clydebank. 
Mr BOBT. Eluot, B.Sc, Engineering Student, 25 St. Vincent Cresct. 
Mr William Linton, Ship Draughtsman, 1 Carmichael St, Gov^an. 
Mr Fred. Lobnitz, Engineer Apprentice, 55 Thomson St, Govan. 
Mr Frederick William ZdCKER, Engineering Drau^tsman, 139 
West Bridgend, Dumbarton. 



The Twenty-Eighth Annual General Meeting of the Insti- 
tution was held in the Hall of the Institution, 207 Bath Street, on 
Tuesday, the 28th April, 1885, at 8 P.M. 

Professor James Thomson, C.E., LL.D., &c.. President, in the Chair. 

Tlie Minute of General Meeting of 24th March, 1885, was read 
and approved and signed by the President 

The President having to leave on account of another engagement^ 
vacated the Chair in favour of Mr Charles C. Lindsay, C.E., Vice- 
President 

The Treasurer's Annual Financial Statement was submitted and 
adopted. 

The Library Committee's Report as to Library Books was read 
and adopted. 

The proposal by the Council to alter the Bye-Laws dealing 
with premiums for Papers read, was, on the motion of Mr 
Henry Dyer, seconded by Mr John Mayer, unanimously adopted ; 
the alteration is a^ follows: — *^ The Council may recommend pre- 



Min/uies of Proceedings, 281 

miams of books in lieu of, or in addition to, the Qold Medals. The 
values of such premiums of books to be determined by the Council." 

The awards for Papers read Session 1883-84 were then made. 

The Institution Medal was awarded to Mr Ralph Moorb for his 
Paper on " Cable Tramways/' and the Marine Engineering Medal 
to Mr J. H. Biles for his Paper on ''The Stability of Ships at 
Launching " 

A premium of Books was awarded Mr B. L. Weighton for his 
paper on ** The Compound Engine Viewed in its Economical Aspect." 

A premium of Books was also awarded Messrs F. P. Purvis and 
B. KiNDERMANN for their Paper on " Approximation to Curves of 
Stability from Data for Known Ships." 

The election of Members of Council then took place. 

Mr C. P. Hogg and Mr John Inglis, Jun., were unanimously 
elected Yice-Presidents of the Institution. 

The following gentlemen were, by a majority of votes, elected 
Councillors :— Professor Elgar, LL.D., Charles C. Lindsay, C.E., 
John Henderson, Jun., Henry Dyer, C.E., M.A., and George 
Russell. 

Mr James M. Gale, C.E., was unanimously re-elected Treasurer. 

Mr John Thohson was unanimonsly re-elected to represent the 
Institution at the Council of the College of Science and Arts. 

Proposals by Mr George Russell and Mr Henry Dyer, relating 
to membership and office-bearers, were remitted to the Council for 
consideration. 

The discussion of Mr John Mayer's Paper on " A Continuous 
Regenerative Gas Kiln for Burning Fire-bricks, Pottery, &c.," was 
resumed and terminated. 

The continued discussion of Mr Staveley Taylor's paper on 

''The Butt Fastenings of Iron Vessels" was deferred till First 

General Meeting of next Session. 

37 



282 Minutes of Proceedings. 

The Papers by Mr Alexander Findla.y on '^ Americaii Railwaiy 
Freight Cars," and by Mr Andrew 8. Bigoart on " Sinking &£ 
Cylinders by Pontoons for the Tay Bridge," were held as read, the 
Papers to be printed and the discossion taken at First GrenersI 
Meeting of next Session. 

The Chairman announced that the candidates balloted for hid 
been elected, the names of these gentlemen being as follows : — 

AS MEMBERS *.— 

Mr John Auld, Mechanical Engineer, Whitevale Foundry. 

Mr Walter Brown, Chief Draughtsman, London Works, Benfrev. 

Mr Peter Tayloii, Shipyard Manager, London Works, Renfrew. 



284 






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190 



Deceased Members. 



Daring the Session 1884-85 the Institution has lost from the Boll 
of Membership the following gentlemen who have been long con- 
nected with the Institution and took an interest in its operations. 
These are : — 

Captain Wif. Brown, Glasgow, who joined the Institution as an 
Associate in 1877. 

Mr Archibald Gray, Dairy, who joined the Institution as a 
Member in 1861. 

Mr J. I. M'Derment, Ayr, who joined the Institution in 1857, the 
year in which it was founded. 

Mr Walter Neuron, of Summerlee, who was one of the Original 
Members of the Institution. 

Mr Walter Neii^gn, as an Original Member, has been con- 
nected with the Institution since its commencement in 1857. 
While under his father, Mr John Neilson, in the Oakbank Foundry, 
he had a varied experience of engineering work, the " Fairy Queen," 
the first iron steamer plying on the Clyde, having been built at the 
Oakbank Foundry, and taken from thence to the river and launched 
in 1831. Mr Neilson afterwards became connected with the pig- 
iron manufacture, and was one of the partners of the Summerlee 
Iron Coy. 



DONATIONS TO LIBRARY. 



Resdts of Trials made in Her Majesty's Screw Ships and Vessels 
from 1 880-84. From the Lords Commissioners of the Admiralty. 

The Forth Bridge, by B. Baker, Esq. From the Author. 

Life of Graham, by Dr H Angas Smith. From J. J. Coleman, Esq., 
F.C.S. 

Inaogoral Address — Chairof Naval Architecture and Marine Engineer- 
ing, Glasgow University — by Professor Elgar, LL.D. From 
the Author. 

Guide Book of Canada. From the Canadian Pacific Railway Co. 

Hydraulic Pumping, by D. Johnston, Esq. From the Author. 

Chain Cables and Chains, by Thomas W. Traill, Esq., C.E., R.N. 
From the Author, 

Descriptive Sketch of Canada, with Maps, &c. From the Directors 
of the Geological Survey of Canada, 

Map of Canada. From the Directors of the Canadian Pacific 
Railway Co. 

Sketch of Rise and Progress of Lloyd s Register. From the Chair- 
man and Committee of Lloyd's Register of British Shipping. 



LIST OF NEW BOOKS RECENTLY ADDED TO THE 
LIBRARY. 

Spon's Dictionary of Engineering, in Eight Divisions. 

Supplement to do., in Three Divisions. 

Tredgold's Elementary Principles of Carpentery. Ed. by E. W. Tarn. 

Sanitary Engineering. Baldwin Latham. 

Disposal of Sewage. Henry Robinson. 

The Municipal and Sanitary Engineers* Handbook. Percy Boulnois. 

38 



202 

Electricity, Its Theory, Sources, and Application. J. T. Spragae, 

Fuel and Water. Professor Schwackhofer and W. R. Browne, M.A. 

Civil and Hydraulic Engineering. Henry Law. Ed. by D. K, Clarke. 

Manual of Electro-Metallurgy. James Napier. 

The Stability of Ships. Sir E. J. Ueed. 

The Steam Engine. Arthur Rigg. 

Cresy^s Civil Engineering. 

Manual of Telegraph Construction. J. C. Douglas. 

Strength of Iron and Steel. Professor Thurston. 

Tunnelling. Drinker. 

Heat Thomas Box. 

Manual of Geology, Vol. I. Phillips. 

Cotterill's Mechanics. 



The Institution Exchanges Transacttions with the Foi^ 
LOWING Societies: — 
Institution of Civil Engineers. 
Institution of Civil Engineers of Ireland. 
Institution of Mechanical Engineers. 
Institution of Naval Architects. 
Institute of Mining and Mechanical Engineers. 
Institute of Mining, Civil, and Mechanical Engineers. 
Iron and Steel Institute. 
Liverpool Polytechnic Society. 
Literary and Philosophical Society of Manchester. 
Mining'Institute of Scotland. 
Patent Office, London. 
Philosophical Society of Glasgow. 
Royal Scottish Society of Arts. 
Royal Dublin Society. 
South Wales Institute'of Engineers. 
Society of Engineers. 
Society'of Arts. 
Association of Employers, Foremen, and Draughtsmen Manchesten 



. 293 

Amflrioan Soeietj of Oiyil Engiiieera. 

€reological Survey of Canada. 

Smithsonian Institution, U.S.A. 

Stevens Institute of Technology, U.S. A, 

Bureau of Steam Engineering, Xavy Department, U.S.A. 

Royal Society of Tasmania. 

Royal Society of Victoria. 

Royal Academy of Sciences, Lisbon. 

Societe des Ingenieurs Givils de France. 

Soci^t^ Industrielle de Mulhouse. 

Soci6t6 d'Encouragement pour I'lndustrie Nationale. 

Soci^t^ des Anciens El^ves des Ecdles Nationales d'Arts et Metiers. 

Soci^t^ des Sciences Physiques et Naturelles de Bordeaux. 

Austrian Engineers' and Architects' Society, Vienna. 

Slngineers and Architects' Society of Naples. 

The Association of Civil Engineers of Belgium. 

Master Car Builders' Association, U.S.A. 



PU^BLICATIONS RECEIVED PERIODICALLY IN EXCHANGE FOR 

iNSTrrunoN Transactions: — 



Annales Industrielles. 
Annales de la Propriety 

Industrielle. 
Colliery Guardian. 
Engineering. 
Iron. 
Iron and Coal Trades' Review. 



Journal de L'Ecole Polytechnic. 

Mining Journal. 

Nature. 

Revue Industrielle. 

The Engineer. 

The Steamship. 

The Machinery Market. 



The Marine Engineer. 

The American ManufiEtcturer and Iron World. 

The Contract Journal. 



The library of the Institution, at the Rooms, 207 Bath Street, is 
open daily from 9-30 a.m. till 8 p.m. ; on Meeting Nights of the 
Institution and Philosophical Society, till 10 p.m. ; and on Saturdays 



294 

till 2 p.in. Books will be lent out on presentation of Memberahip 
Card to the Sub- Librarian. 

Members have also the privilege of consulting the Books in the 
Library of the Philosophical Society. 

The use of Library and Heading Koom is open to Members. 
Associates, and Graduates. 

The Portrait Album lies in the Library for the reception of Mem- 
bers' Portraits. 

Members are requested when forwarding Portraits to attach 
Signature to bottom of Carte. 

The Library is open during Summer from 9-30 a.m. till 5 p.m.: 
and on Saturdays till 2 p.m. 

Copies of Catalogue of Books in Library may be had from the 
Secretary. 

Members of this Institution, who may be temporarily resident in 
Edinburgh, will, on application to the Secretary of the Royal 
Scottish Society of Arts, at his Office, 117 George Street, be fumishe<l 
with Billets for attending the Meetings of that Society. 

The Meetings of the Royal Scottish Society of Arts are held on 
the 2nd and 4th Mondays of each Month, from November till April, 
with the exception of the 4th Monday of December. 



LIST 

OF 

HOVOMAT MEMBBBS, HEHBEBS, AS80CUTES, IKD OMSUITES 

OF THE 

|nstittrti0n of ftngiiwjers anb ^feipbnUim in ^Mani 

(INCORPORATED), 
SESSION 1884-8 5. 



HONOEAKY MEMBERS. 

James Prescott Joule, LL.D., F.R.S., 12 Wardle Road, Sale, 
near Manchester. 

Professor Charles Piazzi Smyth, F.R.S.E., Astronomer- Royal for 
Scotland, 15 Royal Terrace, Edinburgh. 

Professor Sir William Thomson, A.M., LL.D., D.C.L., F.R.SS.L. 
and E., Professor of Natural Philosophy in the University of 
Glasgow. 

Professor R. Clausius, the University, Bonn, Prussia. 

Sir Joseph Whitworth, Bart., C.E., LL.D., F.R.S., Manchester. 

Professor John Tyndall, D.C.L., LL D., F.R.S., &c.. Royal Insti- 
tution, London. 

His Grace the Duke of Sutherland, Trentham, Stoke-upon-Trent. 

Sir Wm. G. Armstrong, C.B., LL.D., D.C.L., F.R.S., Newcastle- 
on-Tyne. 

Professor H, VoN Helmholtz, Berlin, 



296 



M€tfi)biTi. 



DATE OF BLXCTXOll. 

1883, Mar. 20: Geo. A. 
1859, Jan. 19: James 



MEMBERS. 

Agnew, 
*AitkeD, Jan., 



1860, Dec 2G: William Alton, 
Original; William Alexander, 

Original: Alexander Allan, 



1872, Feb. 27: A. B. 


Allan, C.E., 


1869, Jan. 20: William 


Allan, 


1864, Dec. 21: James B. 


Altiott, 


G. 1865, Feb. 15: j^^^ 
M. 1877, Dec. 18:) ^°'-^- 


Alston, 


1880, Nov. 23: Thomas 


Anderson, 



G. 1874, Feb. 24:) J 
M.1880,Nov.23:r*°^^ 



Anderson, 



1860, Nov. 28: Robert Angus, 

1883, Dec. 18: J. Cameron Arrol, 

1875, Dec. 2 1 : Thomas A. Arrol, 
iFict'FruidefU.) 

1885, Jan. 27: William Arrol, 
Original: David Anld, 

1885, Apr. 28: John Auld, 



1881, Oct. 25: Allan W. Baird, 



3 Gladstone Terrace, Govait 
Shipbuilder, Whitetnch, 

Glasgow. 
Sandford Lodge, PeterheaiL 

23 India Street, Glasgow. 
Glen House, The Vallej, 

Scarborough. 

Burgh Surveyor, Burgh 
Chambers, Govaa. 

Scotland House, Sunder- 
land. 

The Park, NottinghanL 

24 Bumbank Gardens. 
Glasgow. 

Government Dockyard 

Bombay. 
100 Clyde St., Glasgow. 

Lugar Ironworks,Cumnock. 

18 Blythswood Square, 
Glasgow. 

18 Blythswood Square, 
Glasgow. 

10 Oakley Ter., Glasgow. 

65 Rochester St., Glasgow. 

White vale Foundry," Glas- 
gow. 

Eastwood Villa, St An- 
drew's Drive, Pollok- 

Ehieldis. 



Names marked thus * were Members of Scottish Shipbailders Atsoeiation at 
IneorporatioB with Institatioo, 1865. 

Names mnrked thnst sre Life Members. 



1880, Feb. 24: WilliAm N. Bain, 



29: 



1873, Apr. 22: H. W. 
1858, Dec. 22: Andrew 



CoDingwood, PoUokshklds, 
Glasgow. 
Ball, CranRtonhill Engine Works, 

Glasgow. 
Barclay, F.R.A.S., Caledonian Fonndrj, 
Kilmarnock. 
1876, Jan. 25: James Barr, 

1882, Mar. 21: Prof.Archd. Barr, B.Sc, C.B., The Yorkshire College, 

Leeds. 
1868, Apr. 22: Edward Barrow, 



1881, Mar. 22: George H. Baxter, 
187j, Jan. 26: Charles Bell, 
David *Bel), 

1868, Feb. 12: Edward M. Bell, 
1880, Mar. 23: Imrie Bell, C.E., 



Rne de la Proyince, Snd, 
Antwerp, Belginm. 

Bamage & Fergnson,Leith. 

4 Clifton Place, Glasgow. 

Shipbuilder, Yoker, near 
Glasgow. 

Tinplate Works,Coatbridge. 

1 Victoria Street, West- 

minster, London, S.W. 

1880, Nov. 2 : Alfred G. Berry, 33 Carnarvon St., Glasgow. 

G. 1883, Mar. 20: ) ..^ ^ w,,^.rf n i? ^^^^ ^"^ge Work8,Sonth 
M. 1884, Nov. 25: \ ^""^'^^ S. Biggart, CB, ^^^^^^^ 

1884,Mar.25:JohnHarvard Biles, Clydebank Shipyard, near 

Glasgow. 

Eagle Foundry, Greenock. 

Shipbuilder, Port-Glasgow. 

127 Trongate, Glasgow. 

38 Elmbank Cres., Glasgow. 

23 Miller Street, Glasgow. 

Ant and Bee Works, West 
Gorton, Manchester. 

13 Royal Crescent, W., 
Glasgow. 
Brand, C.E., 109 Bath Street, Glasgow. 



1866, Dec. 26: Edward 
1864, Oct. 26: Thomas 
1869, Feb. 17: Geo. M*L. 

1867, Mar. 27: James M. 
1883, Jan. 23: Chas. C. 



Blackmore, 
Blackwood, 
Blair, 
Blair, 
Bone, C.E., 



1883, Oct. 23: William L. Bone, 
1874, Jan. 27: Howard Bowser, 



1880, Mar. 23: James 

G. 1873, Dec. 23: ) , ^^ 
M.1884, Jan.22:r*™«' 



Broadfoot, 55 Finnieston St., Glasgow. 



29« 



JHfenibers, 



1865, Apr. 26: Walter 

1859, Feb. 16: Andrew 
1885, Apr. 28: Walter 
1880, Dec. 21: WilKam 

G. 1874, Jan. 27:)^.,,. 
M.1884; Jan. 22:1^^*'^*°^ 

1858, Mar. 17: James 

1877, Oct, 30: Robert 

1860, Dec. 26: James C. 

1866, Apr. 26: Amedee 

Andrew 

1880, Dec. 21: James W. 

1881, Mar. 22: Thomas 
1884, Jan. 22: Edward H« 



1878, Oct 29: Edward B. 
1878, Dec. 17: James 
1885, Mar. 24: John B. 
1875, Dec. 21: J. C. 
1868, Dec. 23: David 
1859, Nov. 23: Peter 
1862, Jan. 8: John 
1881, Not. 22: John H. 



1859, Oct. 2Q: Robert 

1867, Jan. 30: Albert 

G. 1878, Dec. 23:1 ^, 
M.1883, Oct. 23:1^*'^^ 



•Brock, 


Engine Works, Dumbarton. 


*Brown, 


London Works, Renfrew. 


Brown, 


Castlehill, Renfrew. 


Brown, 


Albion Works, Woodrille 




Street, Goyan, Glasgow. 


Brown, 


61 Queen Street, Renfrew. 


Brownlee, 


2 3 Bumbank G ardens, 




Glasgow. 


Bruce, 


1 2 KeMngroveSt.,Glasgow. 


Bnnten, 


100 CheapsideSt.,Glasgow. 


Bnquet, C.E 


.,15 Ghemiss, St« Martin, 




Pontoise, S. 0. France. 


*Bums, 


Hilton of Burleigh, Milna- 




thort. 


Bnms, 


37 Bentinck St., Glasgow. 


Bart, 


371 New City Rd.,Glasgow. 


Bnshell. 


G 19 Exchange Buildings, 




Liverpool. 


Caird, 


8 Scotland St., Glasgow. 


Caldwell, 


130 Elliot Street, Glasgow. 


Cameron, 


160 Hope Street, Glasgow. 


Cameron, 


24 PoUok Street, Glasgow. 


Carmichael, 


Ward Foundry, Dundee. 


Carmichael. 


Dens Works, Dundee. 


Carrick, 


6 Park Quadrant, Glasgow 


Carrathers, 


Craigmore, Queen Bfary 




Avenue, Crossbill, Glas- 




gow. 


Cassels, 


168 St. Vincent Street^ Glas- 




gow. 


Castel, 


3 Lombard Court, London, 




E.C. 


Chamber§, 


24 Ulster Chambers, Belfast 





MewMTSt 


1883, Jan. 23: John 


Clark, 


1875, Oct. 26: W. J. 


Clark, 


1880, Nov. 2: James 


ClarksoD, 



299 

British India Steam Navi- 
gation Co., Calcutta. 
South wick, near Sunderland. 
Maryhill Engine Works, 
Maryhill, Glasgow. 
1860, Apr. 11: James Clinkskill, 1 Holland Place, Glasgow. 

1884, Feb. 26: James T. Cochran, Duke Street, Birkenhead. 
1881, Oct. 25: George Cockbum, Rhodora Villa, St. An- 

drew's Drive, Pollok- 
shields, Glasgow. 
M 1884' Mar 25- \ ^^^^^^ Connell, Whiteinch, Glasgow. 

Original: Robert Cook, Woodbine Cottage, PoUok- 

shields, Glasgow. 

G. 1876, Jan. 25: \ William M. Cooke, Gourlaj Bros. & Co., Dun- 

M.1884, Jan. 22: J ^^ 

1864, Feb. 17: James Copeland, 16 Pulteney St., Glasgow. 

1864, Jan. 20: William R. Copland, C.E., 146 West Regent Street, 

Glasgow. 
1868, Mar. 11: S. G. G. Copestake, GlasgowLoeoinotiveWorks. 

Little Govan. Glasgow. 
1866, Nov. 28: M*Taggart Cowan, C.E., 109 Bath Street, Glasgow. 

1868, Apr. 22: David Cowan, C.E., Mount Gerald House, Fal- 

kirk. 
1861. Dec. 11: William Cowan, 46 Skene Terrace, Aber- 

deen. 

1883, Dec. 18: Samuel Crawford, Clydebank, near Glasgow. 
1881, Mar. 22: William Crockatt, 2 Marjory Place, Pollok- 

shields, Glasgow. 
1866, Dec, 2Q: James L. CunliiT, Plewlands House, Mcrchis- 

ton. Edinburgh . 
1872, Nov. 26: David Cunniugham, C.E., Harbour Chambers, 

Dundee. 

1884, Dec. 23: Peter N. Cunningham, 5 North East Park Street, 

Glasgow. 

1869, Jan. 20: James Currie, 16 Bernard Street, Leith. 

39 



300 



M&nJbtirs 



G. 187 k Feb. 24:) James Davie, 

M.1882, Dec. 19:J 

1861, Dec. 11: Thomas Davison, 
1864, Feb. 17: St. J. Y. Day, C.E., 
1869, Feb. 17: James Deas, C.E.. 

1882, Dec. 19: J.H.L.Van Deinse, 

1883, Nov. 21: James Denholm, 

1866, Feb. 14: A, C. H. Dekke, 

Peter •Denny, 

1878, Feb. 18: William Denny, 

G. 1878, Dec. 23:) p j. 

M. 1884, Jan. 22: ) ^^^^'^ ^^'^^'^^ 

1878, Mar. 19: Frank W. Dick, 

{Member of Council.) 

G. 1873, Dec24:) t. g * n- 
M. 1878! Jan. 22:r^™^S- ^^^''"' 
1882, Nov. 28: John G. Dobbie, 

1871, Jan. 17: William Dobson, 



1864, Jan. 20: 
1876, Jan. 25: 

1863, Nov. 25: 

1884, Dec. 23: 
1882, Oct. 24: 

1864, Oct. 26: 
1881, Jan. 25: 



James Donald, 

James Donaldson, 

Robert Douglas, 

John W.W. Drysdale, 
Chas. R. Dubs, 

Robert *Duncan, 
(Past President; Vice 

Robert Duncan, 
(Membei' of CouiwiL) 



234 Catbcart Road, CrosB. 
hill, Glasgow. 

248 Bath Street, Glasgow. 

1 1 5 St. YincentSt.,Glasgow. 

Engineer, Clyde Trust, 7 
Crown Gardeii8,Glasgow. 

85 de Rny terkade, Amster- 
dam. 

360 Dumbarton Road, 
Glasgow. 

Shipbuilder, Bergen, Nor- 
way. 

Ilelenslee, Dumbarton. 

Leven Shipy'd, Dumbarton. 

25 North Street* Glasgow 

405 Eglinion Street, Glas- 
gow. 
170 Hope Street, Glasgow. 

British India Steam Naviga- 
tion Co., Mazagon Dock- 
yard. Bombay. 

The Chesters, Jesmond, 
Newcastle-on-Tyne 

Abbey Works, Paisley. 

Fulbar Street, Renfrew. 

Dnnnikier Foundry, Kirk- 
caldy. 

5 Wbitehill Gardens, G'gow. 

G lasgo wLocomoti veWork?, 

Glasgow. 

Shipbuilder, Port-Glasgow. 
rresident,) 

Whitefield Engine Works. 

Govan, Glasgow. 



Members. 



301 



1873, Apr. 22: Robert Duada8,C.E., 3Genni8tonStroet,Qlasgow. 
(Member of Council.) 

1869, Xoy.23; David Jno. Dunlop, Inch Works, Port-Glaagow. 

1877, Jan. 23: John O. Dunlop, 17 Goulton Road, Lower 

Clapton, Loudon. 
1880, Mar. 23: Hugh S. Dunn, Earlston Villa, Capringtou, 

Eilmarnook. 
1879, Dec. 23: Wm. T. Courtier Dutton 30 Gordon Street,:Glasgow. 
1883, Oct. 23: Henry Dyer, C.E., 8 Highburgh Terrace, Dow- 

anhill, Glasgow. 

1876, Oct. 24: Jn. Marshall Easton, Redholm, Helensburgh. 

1885, Feb. 24: Prof. Francis Elgar,LL.D.,P.R.S.E., 17 University 

Gardens, Glasgow. 



1875, Oct. 26: James G. 
John 

Q. 1869, Nov. 23:) j ^ 
M.187H, Mar. 19:^°"" 

1874, Feb. 24: Immer 

1880, Jan. 27: Alexander Findlay, 

^L!88J:5rv:25;}«•W'''^"p•"d''*y' 



1884, Dec. 23: Finlay 

Original: William 

1872, Nov. 26: Thomas 

1883, Dec. 18: Lawson 
1870, Jan. 18: WilUam 



Fairweather,C.E.,B.Sc.,8 Findhorn Place, 

Grange, Edinburgh. 
♦Ferguson, Shipbuilder, Whiteincli, 
Glasgow. 

Ferguson, jun., Shipbuilder, Ijeitli. 

Fielden, 6 Lome Terrace, llolder- 

ness Road, Hull. 
Ilamillon Road, Mother- 
well. 
Ardeer, Stevenston. 

Glengarnock Steel Works, 

Glengarnock. 
77 Renfield St., Glasgow. 
Forrest, M.E., Dumfries Ironworks, Dum- 
fries. 
Forsyth, 10 Grafton Sq., Glasgow. 

Foulis, Engmeer, Corporation Gas 

Works, 42 Virginia St., 
Glasgow. 



Finlayson, 
Forrest, 



302 



Members, 



1880, Nov. 2: Samson Fox, 
1862, No7. 26: Alexander FuUarton, 
1879, Nov. 25: John Frazer, 



1885, Jan. 27: Peter 



Fyfe, 



Leeds Forge, Leeds. 
Yulcan Worka, Paisley. 
P. Henderson & Co., 15 St. 

Vincent Place, Glasgov. 
234 Parliamentary Road, 

Glasgow. 



1858, Nov. 24: James M. Gale, O.E., 
{Past President; Memler of Council, 
and Treasurer.) 



18 02, Jan. tS: Andrew 
1883, Oct. 23: Gilbert H. 
1873, Dec. 23: Bernard 



Garrett, 
Gatow, 



G. 1873, Dec. 23:) a„^.^„ /^;m 
M.1882,Mar.21:r°^^«^ ^''^^' 

18r)9, Nov. 23: Arcliibald *Gi!christ, 

G. 1866, Dec. 26:) James Gilchrist, 

.M.1878, Oct. 29: i (Member of Covncil) 

1859, Dec. 21 : David C. Gloii, 



1868, Nov. 25: Thomas (» oldie, 



1864, Feb. 17: James 
1866, Mar. 28: Gilbert F. 



1 868, Mar. 1 1 : Joseph Goodfello w, 

1858, Dec. 22: Henry 'Gourlay, 

1882, Apr. 25: H. Garrett Gourlay, 

Edwin *Graham, 



1858, Mar. 12: George 



EngineerjCorporationWatfl- 
Works, 23 Miller Street, 
Glasgow. 

Galloway, C.E., St. Enoch Station, Glas- 
gow. 

47 West Cumberland St, 
Glasgow. 

Veritas Office, 29 Waterloo 
Street, Glasgow. 

Rait & Gardiner, Millwali 
Docks, London. 

11 Sandyford PL, Glasgow, 

Stobcross Engine Work.«^ 
FinniestonQuay, GIas*ro w. 

14 Annfield Place, Deimis- 
toun, Glasgow. 

Waverley Mills, Ceres Koad^ 
Cape of Good Hope. 

Ironfounder, Ardrossan. 

Alexandra Buildings, Jaiuev 
Street, Liverpool. 

136 Sackville Place, Stir- 
ling Road, Glasgow. 

Dundee Foundry, Dundee. 

Dundee Foundry, Dundee. 

Osbourne, Graham, & Co,, 
Hylton, Sunderland. 
Graham,C.E., Engineer, Caledonian R«n- 
way, Glasgow, 



Goodwin, 
(.loodwin. 



Memhers, 
1876, Jan. 25: Thomas M. Grant, 



303 



1871, Mar. 28: Thomas Gray, 
1862, Jan. 8: James Gray, 



4 Clayton Terrace, Dennis- 

tonn, Glasgow. 
Chapel Colliery, Kewmaius. 
Pathhead Colliery, Cum- 
nock, Ayrshire. 
1870, Feb. 22: P. B. W. Gross, M.E., 4 Albion Place, Cumberland 

Road, Bristol. 
Groves, 131 Hope Street, Glasgow. 



1881, Dec. 20: L. John 
1879, Nov. 25: Robert 
1872, Feb. 27: A. A. 



1881, Jan. 25: William 
1876, Oct. 24: David 



fHadfield, Hadfield Steel Foundry 

Co., Attercliffe, Sheffield. 

Haddin, C.E.,131 West Regent Street, 

Glasgow. 
Hall, jun., Shipbuilder, Aberdeen. 
Halley, Bnrmeister & Wain, Copen 

hagen, Denmark. 
G. 1873, Dec, 23:? David C. Hamilton, Clyde Shipping Co., 21 
M. 1881, Nov. 22:J {Member of Council) Carlton Pkice, Glasgow. 

G. 1866, Dec. 26:] James Hamilton, jr., Ardedynn, Kelvinside,Glas- 
M.1873, Mar. 18:) 

John 

G.1869,Kov.23:? J. B. 
M.1875,Feb.23:f 

1876, Feb. 22: AV alter 

G.1880, Nov. 2:1 Bruce 
M.1884, Jan.22:) 

1878,Mar. 19: Timothy 

1875, Jan. 26: Peter T. 

G. 1874, Feb. 24:) p ^ 
M. 1880, Nov. 23. r*^- 

1804, Nov. 23: John 





sow. 


Hamilton. 


22 Athole Gardens, Gl'gow. 


Hamond, 


The Victoria Engineering 




Coy., Victoria Works^ 




Stockport. 


Hannah. 


Board of Trade Surveyor, 




7 York Street, Glasgow. 


Harman, 


R. Napier & Sons, Govan, 




Glasgow. 


Harrington, 


61 Gracechurch Street,Lon- 




don, E.C. 


Harris, 


19 WestSt.(S.S.),Glasgow. 


Harvey, 


166 Renfrew St., Glasgow. 


Hastie, 


Kilblain Engine Works, 




Greenock. 



304 Mmbers. 

1871, JaD. 17: William Hastie, Kilblain Engine Works, 

Greenock. 

1879, Nov. 25: A. P. tFTendersou, 30 Lancefield Quay, (rlas- 

gow. 

1877, Feb, 20: David ^Henderson, Meadowside, Partick, Glas- 

gow. 
1873, Jan. 21: John tHenderson,jr.,Meadowside, Partick, Glas- 

gow. 

1879, Nov. 25: JohnL. jHenderson, Westbank House, Partick, 

Glasgow. 

1878, Dec. 17: William Henderson, Meadowaide, Partick, 

Glasgow. 

1880, Nov. 2: WilUam Hender8on,C.E., 12lW.RegentSt^Grgow. 
1870, May 31 : Richard Henigan,C.E., AlmaTerrace,AvenaeRoad, 

Southampton. 

1877, Feb. 20: George Herriot, 7 York Street, Glasgow. 

Laurence *Hill, G.E., 5 Doon Gardens, Hillhead, 

Glasgow. 

1880, Nov. 2: C. P. Hogg, C.E., 175 Hope Street, Glasgow. 

{Member of Council,) 

1883, Mar. 20: John Hogg, Victoria Engine Works. 

Airdrie. 

1880, Mar. 23: F. G. Holmes, C.E., 109 Bath Street, Glasgow. 

1883, Mar. 20: Matthew Holmes, 551 Sanchiehall St, Glas- 

{Member of Council.) ^^^^ 

Original: James Howden, 8 Scotland Street, Glasgow. 

1884, Apr. 22; John G. Hudson, 18 Ajtoun Road., Pollok- 

shields, Glasgow. 
Original: Edmund *Hunt, 87 St. Vincent St., Glasgow. 

1860, Nov. 28: James Hunter, Coltness Iron Works, bj 

Newmams. 

1881, Jan. 25: James Hunter, Aberdeen Iron Works,Aber- 

deen. 
1857, Dec. 23: John Hunter, Dahnellington Iron Works. 

near Ayr. 



k.ir77.?rb:20;}^-S- Hpbp, Buenos Ayres 

Original: John •Inglis, 

1861 , May 1 : John Ingh's, Jan., 

1879, Jan. 21: Thoe. F. Irwin, 



305 



1880, Nov. 2: Lawrence N. Jackson, 

1 875, Dec. 21 : William Jackson, 

1884, Jan. 22: J. Yate John8on,C.l 

1879, Feb. 25: Dayid Johnston, 

1870, Dec. 20: David Jones, 

1883, Jan. 23: F. C. Kelson, 

1872, Mar. 26: Ebenezer Kemp, 

1875, Nov. 23: William Kemp, 
1878, Mar. 19: Ungh Kennedy, 
1877, Jan. 23: John Kennedy, 

1876, Feb. 22: Thomas Kennedy, 

1 876, Oct. 24: Andrew Kerr, C.B., 



64 Warroch Street, Glas- 
gow. 

Point House Shipyard, 
Glasgow. 

2a Tower Chambers, Old 
Ghorchyard, Liverpool. 

Colombo, Ceylon. 

Go van Engine Works, 

Govan, Glasgow. 
!., 115 St. Vincent Street, 

Glasgow. 
6 Osborne Place, Copeland 

Road, Govan, Glasgow. 
Highland Rlwy., Inverness. 

Angra Bank, Waterloo 
Park, Waterloo, Liver- 
pool. . 

Linihouse Engine Works, 
Govan, Glasgow. 

ElIenStEngineeringWorks, 
Govan, Glasgow. 

Redclyffe, Partickhill, Glas- 
gow. 

R. M^Andrew & Co., Suffolk 
House, Laurence Pount- 
ney Hill, London, E.C. 

Water Meter Works, Kil- 
marnock. 

Town Surveyor's Office, 
Warrnambool, Victoria, 
Australia. 



306 



Members. 



David 
1879, Dec. 23: John G. 



Original: 



•Kinghorn, 
Kinghorn, 



1864, Oct. 26: Alex. C. Kirk, 



DaTid *Kirkaldy, 



1885, Jau. 27: Charles A. Knight. 
1880, Mar. 23: Frederick Krebs. 



172 LancefieldSt.,Glasgow. 
2 Alexandra Terrace, Rck^ 

Ferry, Cheshire. 
19 Athole Gardens, HiU- 

bead, Glasgow. 
Testing and Experimentiiu: 

Works, 99 Soathwark 

Street, London, S.E. 
107 Hope Street, Glasgow. 
M.B.M.S.S. Co., Tokia 

Japan. 



1875, Oct. 26: William Lainjr, 
1858, Apr. 14: David I^aidlaw, 

1884, Mar. 25: John Laidlaw. 

1862, Nov. 26: Robert Laidlaw, 

1880, Feb. 24: James Lang, 

1884, Feb. 26: John Lang, Jan., 

Original: James G. *Lawrie, 

(Past President.) 

1 882, Mar 2 1 : Henry A . Lawson, 

1880, Mar. 23: Allison Lennox, 

1878, Mar. 19: John Lennox, 

G. 1873, Dec. 23:) Charles C. Liud8ay,C.E 
M. 1876, Oct. 24: J ( Vice-President.) 

1884, Feb. 26: John List, 

1862, Apr. 2: H. C. Lobnitz, 

1865, Dec. 20: John L. Lumsden, 

1873, Jan. 21: James M. Lyon, M.E., 



17 M' Alpine St., Glasgow. 
Chaseley, SkelmorUe. bj 

Glasgow. 
98 Dundas St., S.S., Gi'gow. 
147 E. Milton St, Glasgow. 
^/o John Lang, 552 St. 

Vincent St, Glasgow. 
Church Street, Johnstone. 
2 Westbourne Terrace. 

Glasgow. 
Craigenly Cottage, Leazic, 

near Glasgow. 
131 W. Regent St.,Glasgow. 
131 W.Regent St,Glasgow. 
., lG7StYincentSt.,Glasgow. 

Messrs D. Currie & Co., 

London. 
Renfrew. 
Alex. Jack & Coy., Sea- 

combe, Cheshire.' 
Engineer and Contractor. 

Singapore. 



Jn69mfitS» 



307 



1862, Oct. 29: 
1884, Dec 23: 
1858, Feb. 17: 
1874, Mar. 24: 



1883, Oct 23: 
1871, Jan. 17: 

1884, Feb. 26: 



John 
John 
David 
Hector 

Hagh 

James 
David 
James 



1880, Nov. 2: James W. Macfarlane, 
Original: 



Walter 
Andrew 



1880, Apr. 27: 

1881, Mar. 22: 



Wm. Rae M*Kaig, 
William A. Mackie, 



1873, Jan. 21: J. B. Affleck M'Kinnel, 
1859, Dec. 21 



; Robert 
Andrew 



1884, Dec. 23: James M^Lellau, 

1858, Nov. 24: Walter 

John 

William 
{Member of Council.) 



1884, Dec. 23 
Original: 
1883, Jan. 23; 
1883, Jar. 23 



: John 
Andrew 
William 
James 



M' Andrew, 17 Park St. East, Glasgow. 
M'Beth, 5 Park St., S.S., Glasgow. 

M'Call, C.B., 160 Hope Street, Glasgow. 
MacGoll, Jas. Jack & Co., Engineers, 

Liverpool. 
•MacColl, Manager, Wear Dock Yard, 

Sunderland. 
M'Creath,C.E., 95 Bath Street, Glasgow. 
M'Cnlloch, Vulcan Works,Kilmamock. 
M'Ewan, Cyclops Foundry, 50 Peel 
Street, London Road, 
Glasgow. 
Valeview House, Overlee, 
Busby. 
MacFarlane, Possil Park, Glasgow. 
*M'Geachan, Newark ShipbuildingTard, 
Port-Glasgow. 
17 Water St, Liverpool. 
3 Broomhill Terrace, Par- 
tick, Glasgow. 
Dumfries Iron Works, Dum- 
fries. 
22 Canal St., S.S., Glasgow. 
Viewfield House, Partick, 

Glasgow. 
10 W. Garden Street, Glas- 
gow. 
M*Lellan, 127 Trongate, Glasgow. 
*M*MillaD, Shipbuilder, Dumbarton. 
•MacMillan, 19 Elgin Terrace, Partick, 

Glasgow. 

M'Neil, Helen St., Govan, Glasgow. 

M'Onie, 1 Scotland Street, Glasgow. 

M'Onie, Jr., 128 West Street, Glasgow. 

M'Ritchie, C.E., Singapore. 
40 



M'Laren, 
*MacIean, 



308 

1864, Oct. 

1875, Dec. 
1884, Apr, 

1876, Jan. 



Members. 



26: Robert ^Maiisel, 
(Past Presidmt.) 

21: Geoi^e Mathewson, 
22: Henry A, Maror, 
25: Waiiam W. May, 



1883, Feb. 20: James 



G, 1876, Oct. 
M. 1882, Nov. 



24: 1 James 
28:/ 

23: William 



1883, Jan. 

1881, Mar. 22: William 

1861, Dec. 



11: Daniel 
James 



Shipbuilder, Whitdncb, 

Glasgow. 
Both well W1cs,Dnnf ermline. 
140 Donglas St., Qli^gow 
142 Fountain Road, Wal- 
ton, Liverpool. 
Meek. 10 Clarence Road, Devon 

shire Park, Birkenhead. 
Meldram,G.E., 3 Elmbank Street, Glas- 
gow. 
Melville,C.E., Caledonian Ry., Bachanan 

Street, Glasgow. 
Menzies, 7 Dean Street, Newcastle- 

on-Tyne. 
Miller, C.B., 204 St Ymcent St. .Glasgow. 



•Miller, 



Partick, 



^- 1873, Dec. 
M. 1881, Nov. 

Original: 

1876, Mar. 



23: 



John F. Miller, 



22 

James B, 
21: James 



1869, Dec. 21: John 



1883, Nov. 
1862, Nov. 
1878, Apr. 

1868, Feb. 

G. 1878, Dec. 
M.1883, Jan. 

1885, Mar, 

1864, Feb. 
1882, Jan. 
1870, Mar. 



21: Joseph 
26: Ralph 
23: Robert H. 



12: Alexander 
5 J;| Robert 
,24:EdmQnd 



17: Hugh 
24: John G. 
22: Wm. T. 



Kelvin Forge, 
Glasgow. 

204 Stobcross St.,Gla8gow. 

45 Scotland St., Glasgow. 
Lloyd's Register,36 Oswald 

Street, Glasgow. 
Montgomerie, Kitson & Co., Airedale 

Foundry, Leeds. 
East Finchley, London. 
Croft Villa, Rutherglen. 
Mount Blue Works, Cam- 

lachie, Glasgow. 
241 W.George St.,GIasgow. 

53 Waterloo St., Glasgow. 

Board of Trade Surveyor, 
7 York Street, Glasgow. 
345 BathCrescent,Glasgow, 
100 Cheapside St., Glasgow. 
36 Oswald Street, Glasgow. 



Mirrlees, 
Mollison, 



Moore, 
Moore, C.E 
Moore, 



Morton, 
Morton, 
Mott, 

Muir, 
tMuir, 
Mumford, 



Members. 



309 



1882, Feb. 21: George Monro, 

1 882, Dec. 1 9 : Robert Monro, 

Original: James Mordoch, 

1880, Jan, 27: William Mordoch, 
1877, Jan. 23: Robert Morray, 

1881, Jan. 25: Henry M. Napier, 



254 Bath Street, Glasgow. 
162 Bochanan St., Glasgow. 
Shipboilder, Port-Glasgow. 
20 Carlton Place, Glasgow. 
25a Coltman Street, HoU. 



1867, Dec. 23: John t*^*pi«r, 
1881, Dec. 20: Robert T. fNapier, 



Walter M. Neilson, 
{Past President.) 



Original: 

1869, Noy. 23: Theod. L. Neish, 



A. 1865, Apr. 26: | R. S. 
M.1879, Oct. 28:5 

1883, Dec. 18: Thomas 
1884,Dec. 23: Wm.H. 

1876, Dec. 19: Richard 

1861, Dec. 11: John 



Shipboilder, Yoker, near 

Glasgow. 
23 Portman Sq., London. 
Shipboilder, Yoker, near 

Glasgow. 
Qoeen's Hm,Kirkcodbright- 

shire. 
78 Finnart St., Greenock. 
•Newall, F.R.S.,F.R.A.S., Ac, Ferndene, 

Gatesheadon-Tyne. 
Nicol, Clydebank, near Glasgow. 

Nisbet, Mavisbank, Partickhill, 

Glasgow. 
Niven, C.B., Dalnottar Hoose, Old Kil- 

patrick. 
Norman, 475 New KeppochhillRoad, 
Glasgow. 



1882, Jan. 24: Robert S. Oliver, C B., Highland Railway Co., 

Inverness. 
1860, Nov. 28: John W. Ormiston, 



1885, Mar. 24: Alex. T. 
1867, Apr. 24: T. R. 

1882, Mar. 21; Geo. S 



Shotts Iron Works, by 
Wishaw. 

Orr, Hall, Rossell, & Co., Aber- 

deen. 

Oswald, The Soothampton Ship 

boilding & Engineering 
Works, Soothampton. 

Packer,F.I.C , Hallside Steel Works, 
Newton, near Ghisgow. 



310 



MtmberB* 



1864, Oct. 26: John 


Page, C,K, 


1 Kersland Ter., Olasgow. 


1876, Apr. 25: WiUiam 


Parker, 


2 White Lion Court, Com- 
hill, London. 


1883,Nov.21:W,L. C. 


Paterson, 


19 St, Vincent Crwccnt, 
Glasgow. 


1877, Apr. 24; Andrew 


Paul, 


Levenford Works, Dam- 
barton. 


1880, Nov. 2: James M. 


PearsoUjCE 


, 8 Duke St., Kilmarnock. 


1866, Dec. 26: William 


Pearce, 


Fairfield Shipyard, €h>Yan, 
Glasgow. 


1868, Dec. 23: Engine 


Perignon,C.E., 105 Bue Faubourg, St. 






Honor6, Paris. 


John 


•Price, 


Ro8eViUa,GatesheadRoad, 
Jarrow-on-Tyne. 


1877, Nov. 20: F. P. 


Purvis, 


Craig Villa, Dumbarton. 


1868,Dec. 23: Henry M. 


Rait, 


155 Fenchurch St.,London. 


1873, Apr. 22: Richard 


Ramage, 


Shipbuilder, Leith. 


1866, Dec. 26: Daniel 


Rankin, 


Eagle Foundry, Greenock. 


1872, Oct 22: David 


Rankine, 


75 West Nile Street, Glas- 
gow. 


1876, Dec. 19: Robert 


Rankin, 


35 Paisley Road, Glasgow. 


1881, Jan. 25: Charles 


Reid, 


Lilymount, Ealmarnock. 


1883, Nov. 21: George W 


. Reid, 


Highland Rly., Invemess. 


1868, Mar. 11: James 


Reid, 


LocomotiveWorks, Spring- 


{Past President.) 


bum, Glasgow. 


1869, Mar. 17: James 


Reid, 


Shipbuilder, Port Glasgow. 


John 


♦Reid, 


Shipbuilder, Port-Glasgow. 


1880, Apr. 27: John 


Rennie, 


Ardrossan Shipbuilding 
Co , Ardrossan, 


a. 1873, Dec. 23:) Charles H 


. Reynolds, 


Cuprum House, Hamilton 


M.1881, Nov.22: 




Ter., Partick, Glasgow, 


1876, Oct. 24: Duncan 


Robertson, 


8 Brighton Place, Govan, 
Glasgow. 


Original; James 


Robertson, 


21 Gower Street, Paisley 



Boady Glasgow. 



1873, Jan. 21: John 



Robertson, 



811 



Grange Knowe, Pollok- 
shields, Glasgow. 
1863, Not. 25: WilKam Robertson,C.E., 123 St. Vincent Street, 

Glasgow. 
Robertson, 42 Aytoan Road, PoUok- 
shields, Glasgow. 
14 Royal Cresct, Glasgow. 



1884, Apr. 22: R. A. 



Original: 

1877, Feb, 

186 J, Dec. 

J. 1864, Nov. 
M. 1870, Jan. 

Original: 

1. 1875, Dec. 
Vf. 1885, Jan. 

1877, Oct 

1. 1858, Dec. 
VI. 1863, Mar. 

1881, Feb. 

1859, Dec. 



Hazltn. R. *Robson, 
{Past President,) 

20: Jno.MacDonaldRoBs, 

11: Richard G 



23:? 
18: 



11 Qneen's Ores., Glasgow. 
21 Greenhead St., Glasgow. 

Alex. Ross, O.B., Lynnwood, Alva. 

231 Elliot Street, Glasgow. 



David *Rowan, 
{Past President.) 



I}; j James 

30: Alexander 

^4;| George 

22: Joseph 
21 : Thomas 



1876, Oct. 24: Peter 



1885, Feb. 24: James 

1883, Feb. 20: John 

7 882, Dec. 19: Prof. Ja^. 

1884, Apr. 22: Andrew 
1872, Jan. 30: James E. 
1881, Jan. 25: John 



Rowan, 

Rnssell, 

Rnssell, 

Rassell, 
*Rassell, 

Samson, 



231 Elliot Street, Glasgow. 

186 North Street, Glasgow. 

Engineer, MotherweU. 

Shipbuilder, Port-Glasgow. 
Albyn Lodge, Bridge of 
Allan. 



1860, Nov. 28: Thos. B. *Seath, 



Board of Trade OflSces, 

Downing Street, London, 

S.W. 

Samuel, jun., 238 Berkeley St., Glasgow. 

Sanderson, Lloyd's Registry, 36 Oswald 

Street, Glasgow. 
Scorgie,F.C.S., Civil Engineering College 
Poona, India. 
56 Greame Street, Glasgow. 
13 Rood Lane, London. 
Whitebank Engine Works, 

Kirkcaldy. 
42 Broomielaw, Glasgow. 



Scott, 
Scott, 
Scott, 



312 



Members* 



1875, Jan. 26: Alexander Shanks, 

1 858, Not. 24 : William Simons, 

1862, Jan. 22: Alexander Simpson^CE 

1871, Mar. 28: Hugh SmeUie, 

Original: Alexander Smith, 

1880, Not. 2: Alexander Smith, 



1869, Mar. 1 7 : David S. Smith, 
1859, Jan. 19: George Smith, 
1871, Dee. 11: Hugh 



G. 1868, Dec. 23:) Hugh 
M.1874, Oct. 27:1 



Smith, 
Smith, 



1878, May 14: James Smith, 

1870, Feb. 22: Edward Snowball, 



1883, Oct. 
1883, Dec. 

1881, Not. 

1867, Jan. 
1874, Oct. 

G. 1873, Dec. 
M. 1882, Oct. 

1866, Nov. 



23: Andrew 

18: Alex. E. 

John 

22: Alex. 
{Member 

30: Duncan 

27: Peter 
{Member 

g:}w.B. 

, 28: James 



Sproul, 

tStepben, 

t*Stephen, 

Steven, 
of Council.) 

Stewart, 

Stewart, 
of CoundL) 

Stewart, 

Stirling, 



Original: Patrick Stirling, 



Belgrade^ Ayton Road, Pol- 
lokshields, Glasgow. 

Renfrew. 
,, 175 Hope Street, Glasgow. 

Belmont Grange Terrace, 
Kilmarnock. 

57 Cook Street, Glasgow. 

1 BraesideTerrace^Maxwel] 
Rd., Pollokshields, Glas- 
gow. 

Hellenic Steam NavigatioD 

Co., Syra, Greece- 
Kennedy Street, Parliamen- 
tary Road, Glasgow. 

9 Kelvinside Terrace, North 
Kelvinside, Glasgow. 

07 WelKngton Street, 
Glasgow. 

40 Margaret St, Greenock. 

Engineer, Hyde Park Loco- 
motive Works, Spring- 
bnm, Glasgow. 

Palmerston Blds.,OreeQocL 

12 Park Terrace, Glasgow. 

Linthonse, Go van, Glasgow. 

Provanside, Glasgow. 

47 SunmierStreet,Ghi8gow. 
53 RenfieldStreet,Gla8gow. 

1 Scotland Street, Glasgow. 

Loco. Engmeer, S. Eastern 
Ry., Ashford, Kent 

The Great Northern Rail- 
way, Doncaster. 



1 881 , Jan. 25 : Walter Stoddart, 
1 864, Nov. 23 : Edward Strong, 
1877, Jan. 23: James Sjme, 



1879, Oct. 28: 
1882, Apr. 25: 
1885, Apr. 28: 
1879, Mar. 25: 



James Tait, C.E., 

Alex. M. Taylor, 

Peter Taylor, 

Staveley Taylor, 



1873, Dee. 23: B. L. Tessier, 



1885, Jan, 27: 
1882, Apr. 25 



George W, Thode, 
Geo. P. Thomson, 



1883, Dec. 18: George Thomson, 

1874, Xov. 24: Prof. James Thomson, C. 

{President.) 

1868, Feb, 12: James M. Thomson, 
1882, Mar. 21: James R. Thomson, 

1868, May 20: John Thomson, 

1876, Feb. 22: John Thomson, 

1875, Jan. 26: Robert S. Thomson, 

1864, Feb. 17: W. R. M. Thomson, 

1878, May 14: W. B. Thompson, 

Original: Thomas C. Thorburn, 



313 

Caledonian Railway, Car- 
stairs. 

% Kent Cottage, Qneen's 
Cres., Sonthsea, Hants. 

8 GlenaTon Ter., Partick, 
Glasgow. 

Wishaw. 

Java Cottage, Lenzie. 
59 Queen Street, Renfrew. 
Rassell & Co., Shipbuilders, 

Greenock. 
Veritas Office, 29 Waterloo 

Street, Glasgow. 
107 Hope Street, Glasgow. 
Clydebank Shipbuilding 

Yard, Glasgow. 

9 Buckingham Ter. , Partick, 

Glasgow. 
B., LLJD., F.R.SS.L. & E., 
2 Florentine Gardens, 
Hillhead Street.Glasgow. 

36 Finnieston St., Glasgow. 

Clydebank Foundry, Glas- 
gow. 

36 Finnieston St., Glasgow. 

147 East Milton Street, 
Glasgow, 

3 Melrose Street, Queen's 
Crescent, Glasgow. 

96 Buchanan Street, Glas- 
gow. 

Tay View, Broughty Ferry. 

35 HamiltonSquare,Birken- 
head. 



314 



M0fhbtr$» 



1874, Oct. 27: Prof. R. H- Thurston, M.B., C.B., Sbley Golkge, Cw- 

nell Universityy Ithaca, 
U.S.A. 

1875, Not. 23: John Tnrnbnlljan., Consalting En^neer, 2^5 

Bath Street, Glasgow. 

1876, Nov. 21: Alexander Tomball, 15 Whitehill Terrace, Dea- 

nistonn, Glasgow. 
Tamer, Managing Engmeer,Caiiadi 

Works, Birkenhead. 
Tweedy, Neptune Works, Newcastie- 

on-Tjme- 
1880, Not. 2: Ralph H. Tweddell, 14 Delahay Street^ West- 
minster, London. 

1865, Apr, 26: W, W. Urquhart, BIaeknessFoandry,Dnndee. 



1876, Jan. 25: Henry 
1880, Apr. 27: Jolin 



1883, Jan. 23: Peter 



Wallace, 



1885, Mar. 24: W. Carlile Wallace, 
1875, Mar. 23: G. L. Watson, 



1864, Mar. 16: W. R, 

1883, Jan. 23: D. W. 
John 

1874, Dec. 22: George 

1874, Dec. 22: James 



Watson, 

Watt, 
♦WeUd, 



25 Argyle Place, Partict 

Glasgow. 
Maryland, Dumbarton. 
108 W. Regent St., Glas- 
gow. 
16 Woodlands Ter., Glas- 
gow. 
58 Union Street, Glasgoir. 
Underwriter, Exchange. 
Glasgow. ^ 

Weir, M.E., 1 8 Millbrae Ores., Langside, 

Glasgow. 
Weir, M.E., Silver Bank, CambuslaD^. 
near Glasgow. 
M 1 884' Feb' 26- } Gliomas D. Weir, C.E., 97 W. Regent St, Gksgow. 
1869, Feb. 17: Thomas M. Welsh, 63 St. Vincent Ores., Glas- 

gow. 
1868, Dec. 23: Henry H. West, 13a Exchange Buildings, 

Liverpool. 



Mefmhers. 316 

1883, Feb, 20: Richard S. White, Shipboilder, Sir Wm. Arm- 

|troDg, Mitchell, & Co., 
Newcastle-on-Tyne. 

1884, Not. 25: John Wildridge, Consoltiiig Engineer, 

Sydney. 

1876, Oct. 24: Francis W. Willcox, 45 West Snnniside, Sun- 
derland. 

1884, Dec. 23: James Williamson, Barclay, Cnrle, & Co., 

Whiteinch. 

1883, Feb. 20: Robert Williamson, Lang & Williamson, En- 
gineers, &c., Newport, 
Mon. 

1878, Oct. 29: Thomas Williamson, Netherton House, Wishaw. 

Alex. H. ♦Wilson, Aberdeen Iron Works, 

Aberdeen. 
1868, Dec. 23: James Wilson, C.E., Water Works, Greenock. 

1870, Feb. 22: J(»hn Wilson, Wellfield House, Spring- 

bum, Glasgow. 
1858, Jan, 20: Thomas t*Wingate, Viewfield, Partick. 
G . 1878, Dec. 23: ) j^^^^^ ^ y.^ Hartlepool Engine Works, 

M. 1884, Jan. 22:) ^ ' Hartlepool. 

1879, Oct, 28: John Young, Phoenix Iron Works, Glas- 

gow. 
1 867, Nov. 27: John Young, Galbraith Street, Stobcross, 



Glasgow. 



ASSOCIATES. 



Thomas "Aitken, 8 Commercial Street, Leith. 

Andrew •Armour, 68 Anderston Quay, Glas- 

gow. 



Names marked thos * were AssooiaioB of Scottish ShipbdlderB' AMoclation at 
Bcorporatioii with InatiivtioD, 1865. 

41 



816 AtBodiates. 

1888, Oct. 28: John Barr, Secretary to Glenfield Co, 

KilmarnocL 

1882, Dec. 19: Wm. Begg, 47 WestCmnberland Street, 

Glasgow. 

1882, Jan. 24: John Black, 4AlexandraTerraoe,GovaD. 

Glasgow. 

1884, Dec. 23: W. S. C, Blackley, 10 HamOton Cresceiit, Par- 

tick. 
1876, Jan, 25: John Brown, B.Sc., 11 Somerset Place^GUsgow. 

1865, Jan. 18: John Bryce, Sweethope Cottage, N. Mil- 

ton Road, Donoon. 

1880, Dec. 21: John Cassells 56 Cook Street, Glasgow. 

1870, Dec. 20: Joseph J. Coleman, P,C.S., Ardarroch, Bearsden, by 

Glasgow. 

1885, Feb. 24: Robert Darliog, 5 Snmmerside Place, Leitk 

1859, Nov. 23: Arch, Orr Bwmg, M.P., 2 W. Regent St., Glasgow. 

1863, Mar. 18: Robert Gardner, 52 North Frederick StreeU 

Glasgow. 
1885. Mar. 24: James S. Gardner, 52 North Frederick Stieet 

Glasgow. 

1860, Jan. 18: George T. Hendry, 79 Gt. Clyde St., Glasgow. 

1882, Oct. 24: Wm. A. Kinghorn, 6 Golebrooke St, Hillhead, 

Glasgow. 

1864, Dec. 21: Anderson Kirkwood,LL.D., 7 MeMUeTer., Stirling. 

1878, Oct. 29: John Langlands, 88 Gt. Clyde St., Glasgow. 

1884, Feb. 26: C. R. Lemkes, 198 Hope Street, Glasgow. 

1873, Feb. 18: John Mayer,F.C.S. 2 Clarinda Terrace, Pollok- 

shields, Glasgow. 

1874, Mar. 24: James B, Mercer, Bronghton Copper Works 

Manchester. 



Assodakf. 



317 



Gteorge •Miller 
1865, Dec. 20: John Morgan 

188S, Dec 18: W, M*l7or Morison, 



James S. *Napier, 
John Phillips, 

1869, Nov. 28: Capt. John Rankme, 

1867, Dec. 11: William H. Richardson, 

1882, Dec. 19: Colin Wm. Scott, 

1876, Jan. 25: George Smith, 

John *Smith, 



Malcolm M*N. *Walker, 
H. J. *Wat8on, 

T. 'Westhorp, 

1882, Dec. 19: John D. Young, 
William ♦Young, 



1 WeDesley Place, Ghwgow. 
Springfield House, Bishop- 

Griggs, Glasgow. 
Mayfield, Marine Place, 

Rothesay. 

83 Oswald Street, Glasgow. 

17 Anderston Quay, Glas- 
gow. 

81 Airlie Terrace, PoUok- 

shields, Glasgow. 
19 Kyle Street, Glasgow. 

30 Buchanan St., Glasgow. 
45 West Nile St., Glasgow. 
AberdeenSteam Navigation 
Co., Aberdeen. 

45 Clyde Place, Glasgow 
5 Oswald Street, Glasgow. 
West India Road, London. 

141 Buchanan St., Glasgow 
Galbraith Street,Stobcross, 
Glasgow. 



GRADUATES. 



1884, Dec. 28: Arthur 0. Auden, 
1882, Nov, 28: William H. Agnew, 
1880, Nov. 2: James Aitken, 



9 Carmichael St., Gtovau. 
70 Grant Street, Glasgow. 
142 Cromwell Rd., Patri 
croft, Manchester. 



318 

1880, Feb. 24: George 



OradwUes. 
Almond, 



Belmont, Bolton-le-Moors, 
Lancashire. 



1877, Nov. 20: James T. Baxter, 



1883, Dec. 18: Seymour H. Beale, 
1871, Feb. 21: W. S. Beck, 

1883, Dec. 18: Ladwig Benjamin, 



9 Brighton Terraco, Cope- 
land Road, Grovan. 

Banbnry, Ozon. 

246 Bath Street, aiasgov. 

11 Normandy Street, Upper, 
Parliament St., LirerpooL 

1882, Feb. 21: Alfred G. Berry, jun., 33 Carnarvon St., Glasgow. 
1885, Mar. 21: Alexander Bishop, 3 Germiston St, Glasgow. 

1883, Dec. 18: David Blair, Allan Line Works, Mavis- 
bank Qaay, Glasgow. 

6 Alfred Terrace, Haihead, 
Glasgow. 

Clntha Ironworks, Glasgow. 

M. Langlands & Sons, Por- 
ter Street, Liverpool. 

11 Mount Pleasant Road 
Strond Green, London, N. 

9 Brighton Place, Goran 
Glasgow. 

Castlehill House, Renfrew. 

6 Oh'ig Terrace, Glencaim 
Drive, Pollok8hields,61as- 
gow. 

2 Carmichael Street, 
Govan. 

6 Hamilton Place, Clyde- 
bank. 
1881, Jan. 25: Matthew T. Brown, B.Sc, 33 Hope Street, Glasgow. 
1872, Oct. 22: Hartvig Burmeister, 7o Rahr & Raundrap, 14 

Brown St., Manchester. 
1876, Dec. 19: Lindsay Burnet, Moore Park BoUeir Works. 

Govan, Glasgow. 



1884, Jan. 22: George Blair, jun., 

1884, Jan. 22: Henry Blair, 

1880, Mar. 23: Alexander Bowie, 

1878, Dec. 17: Rowland Brittain, 

1883, Apr. 24: Arthur R. Brown, 



1876, Jan. 25: A. M*N. 
1879,Feb.25: Alex. T. 



Brown, 
Brown, 



1883, Dec. 18: Bben. H. Brown, 
1885, Mar. 24: Matthew B. Brown, 



Oraduates. 



319 



1882, Dec. 19: William T. Calderwood, 6 Smith Street, Hillhead, 

Glasgow. 

1882, Dea 19: Hagh Campbell, Leeds. 

1884, Feb. 26: John Cleland,B.Sc., Woodhead Cottage, Old 

Monkland. 

1884, Feb. 26: Arthur S. Clerk, 



9 Carmichael St., Govan, 
Glasgow. 
1881, Nov. 22: Alfred A. R. Clinkskill, 1 Holland Place, Glasgow. 
1884, Feb. 26: Alexander Conner, 
1877, Dec 18: James Conner, 



9 Scott Street, Glasgow. 
Isle of Wight Railwaj.San- 

down, England. 
1884, Jan. 22: Alex. M. Copeland, Bellahonston Farm, Paislej 

Road, Glasgow. 
Glasgow. 
2 White Hill Gardens, Den- 

nistonn, Glasgow. 
Earle's Shipbnilding and 

Engineering Co., Hnll. 
1882, Feb, 21: Wm. S. Camming, Blackhill, by Parkhead, 



1 874, Feb. 24: Andrew Corbett, 
1880, Dec. 21: Sinclair Conper, 

1880, Nov. 23: James M. Croom, 



1882, Mar 21: Alex. 
1884, Jan. 22: James Dalziel, 

1883, Apr. 24: Alexander Darling, 



Glasgow. 
Canningham, Glasgow. 



1 19 Sandyford Street, Glas- 

gow. 
Upper Assam Tea Coy., 
Maijen Dilbrngdah, Upper 
Assam, India. 
Davidson, 24 Dixon Avenue, Crossbill, 
Glasgow. 
Broomhilllronwks. ,Glasgow 
5 Pembroke Square, Ken- 
sington, London. 
1888, Dec. 18: William Denholm, Glasgow. 
1883, Feb. 10: Lewis M. T. Deveria, Mansfield Cot., Kilwinning. 

1882, Oct. 24: Daniel Doaglas, Earless Shipboilding Co., 

HnU. 



1881, Mar. 22: David 



1885, Feb. 24: William S. Dawson, 
1879, Oct. 28: Jonathan L. Dean, 



320 



Oraduaies. 



1880, Not. 2: Geo. C. Douglas, 

1882, Oct. 24: John P. Douglas, 

1883, Oct. 23: HarFj W. Downes, 



1884, Jau. 22; William Dunlop, 



Douglas Fonndrjy Dundee. 

18 Meadowpark Street, 
Dennistonn. 

Claremont House, Alpha 
Road, New Gross, Lon- 
don, S.E. 

961 Qovan Road, Glasgow 



1882, Dec. 19: A. Von 
1885, Mar. 24: Robert 



Eckermann, 91 Pollok Street, GHasgow. 
Elliot, B.Sc, The Engineers' Olab, 10 
Hare Street, Calcutta 



1878, Jan. 22: James R. Faill, 

1882, Feb. 21: Albert E. Fairman, 

1880, Dec. 21 : Henry M. Fellows, 

1883, Dec. 18: John James Ferguson, 

1884, Jan. 22; Thomas Q. Ferguson, 

1881, Feb. 22: William Ferguson, 

1885, Jan. 27: Wm. D. Ferguson, 
1881, Nov. 22: Charles J. Findlay, 

1883, Oct. 23: Duncan Finlayson, 

1869, Oct. 26: F. P. Fletcher, 



Craig-en-Callie, Ayr. 

21 St, Bede's Terrace, Sun- 

, derland. 
Westboume Lodge, Great 

Yarmouth. 
8 Walworth Ter., Glasgow. 
1 4 Queen's Cres., Glasgow. 
Larkfield, Partick, Glasgow. 
63 Finlay Drive, Glasgow. 
10 Belmont Cres., HiUhead, 

Glasgow. 
1 Osborne Place, Govan, 

Glasgow. 
South Russell St, Falkirk. 



1874, Feb. 24: James 


Gillespie, 


1884, Dec. 23: D. C. 


Glen, Jun., 


1885, Jan. 27: Alex. M. 


Gordon, 


1882, Jan. 24: Arthur B. 


Cowan, 


1884, Feb 26: Alexander 


Grade, 



21 Minerva St., Glasgow. 
14 Annfield PL, Glasgow. 
3 Wallace Grove Placc^ 

Paisley Road, Glasgow. 
3 Octavia St.,Port-Glasgow. 
9 Great George Sta^t, fllil- 

head, Glasgow. 



Ovad^aies. 



Ml 



1881, Dec 20: Andrew 
1874, Feb. 24: Archibald 
1881, Feb. 22: James 
1883, Feb. 20: David 
1S82, Nov. ^S: F. N. 
1881, Oct. 26: Charles O. 



1882, Feb. 21: Wm. S. 
1881, Jan. 25: A. G. 

1884, Dec. 23: John 
1873, Dec. 23: Guybon 



1883, Jan. 23: John A. 
1885, Feb. 24: John 



1873, Dec. 23: David Johnston, 

1883, Feb. 20: Eben. E. Kemp, 

1885, Feb. 24: John Lang, 

1882, Jan. 24: Andrew Laing, 

1883,Nov. 21: William R. Lester, 

1 885, Mar. 24 : William Linton, 



Hamilton, 


2 Belmar Terrace, Pollok- 




shields, Glasgow. 


Hamilton, 


New Dock Works, Govan, 




Glasgow. 


Harvey, 


Park Grove Iron Works 




Paisley Road, Glasgow. 


Henderson, 


11 Haybnm Crescent, Par- 




tickhill, Glasgow. 


Henderson, 


1 1 Princes Terrace, Do wan- 




hill, Glasgow. 


Hepburn, 


Ben Boyd Road, Nentral 




Bay,North Shore,Sydney, 




N.S.W. 


Herriot, 


Leonora, Demerara. 


Holms, Jan., 


Hope Park, Partick, Glas- 




gow. 


Howarth, 


87 Bentinck St., Glasgow. 


Hntson, 


EelvinhanghEngine Works, 




Glasgow, 


Inglis, 


23 Park Circus, Glasgow. 


Inglis, 


Bonnington Brae, Edin- 




burgh. 



12 York Street, Glasgow. 

Overbridge, Govan Glas- 
gow. 

6 Elderslie St., Glasgow. 
Glenavon Ter., Crow Road, 

Partick, Glasgow. 
2 Donne Terrace, North 

Woodside, Glasgow. 
1 Carmichael St., Govan. 



822 GrtutfuOes, 

1885, Mar. 24: Fred. Lobnitz, 2 Park Terrace, Olasgow. 

1884, Dec. 23: Robert Logan, 8 Haybum Cies^ Partick. 

1 884, Nov. 25 : Archd. M'Beth, 1 1 1 Govan Road, Glasgow. 

1880, Nov. 2: Patrick F. M-Callum, Fairbank Cottage, Helens- 

burgh. 

1881, Dec. 20: H. M'Coll, jua., 8 Dahneny Terrace, Pollok- 

shields, Glasgow. 

1883, Dec. 18: Peter M'CoU, Stewartville Place, Partick, 

Glasgow. 

1876, Oct. 24: Jno. M. M^Cnrrich, M.A., Dock Engineer's Office, 

Cumberland Basin^Bristol 

1883, Dec. 18: John MacDonald, 293 New City Road, Glas- 

gow, 

1874, Feb. 24: George M'Farlane, 65 Gt. Clyde St., Glasgow. 

1882, Oct. 24: James L. Macfarlane, Meadowbank, Torrance. 

1883, Dec. 18: John Bow McGregor, 22 Church Street, Partick, 

Glasgow. 

1882, Dec. 19: Allan M*Keand, Glasgow. 

1880, Feb. 24: Neil M'Kechnie, 31 Bank Street, Hillhead, 

Glasgow. 

1881, Oct. 25: James Mackenzie, 16 Eelvinhaugh Street, 

Glasgow. 

1883, Jan. 23: Thos. B. Mackenzie, 342 Duke Street, Glasgow. 

1884, Dec. 23: Jas. M'E. M'lntyre, The Crescent, Dalmoir. 
1883, Feb. 26: Robert M^Kiimell, 56 Dundas Street, S.S., 

Glasgow. 

1876, Dec. 19: John M'Kirdy, 21 St. James Square, Edin- 

burgh. 

1883, Dec. 19: Colin D., M'Lachlan, 5 Ibrox Place, Ibrox. 

1875, Dec. 2 1 : Hugh M*Lachlan, 5 DowanhiU Place, Partick , 

Glasgow. 
1880, Nov. 2: Robert M'Laren, jr., Eglinton Foundry, Glasgow. 
1874, Feb. 24: Andrew Maclean, jun.,Viewfield House, Partick, 

Glasgow 



1882, Dec. 19: Peter 

1874, Feb, 24: William 

1885, Jan. 27; John 
1875,Dec.21:A]li8ter 

1879, Oct. 28: Donald 

Ih 4, Dec. 23: Robert 
1884, Dec. 23: W. J. 

1880, Nov. 2:Iyan 

1882, Jan. 24: Robt. Alex. 
1884, Not. 25: Thomas 
1880, Feb. 24: Robert 

1883, Dec. 18: Charles W. 

1880, Feb. 24: James F. 

1881, Jan. 25: Ernest W. 

1881, Oct. 25: John 

1882, Feb. 21: C.J. 

1882, NoY, 28: M.J. 

1884, Feb. 26: Andrew 
1878, May 14: Angus 

1883, Dec. 18: James L. 



Oraduaiei. 


823 


M'Lean, 


Trafalgar Cottage, South 




Queensferry. 


Maclean, 


Viewfield House, Partick, 




Glasgow. 


M'MiUan, 


26 Ashton Ter., Glasgow. 


MWiven, 


Clutha Iron Works, Ver- 




mont Street, Glasgow. 


M'Taggart, 


48 Ovemewton St., Glas- 




gow. 


Mansel, Jan., 


4 Clyde View, Partick. 


Marshall, 


3 Minerva Street, Glasgow. 


Mayor, 


Wincomlee, Low Walker- 




on-Tyne. 


Middleton, 


20 Merryland St, Govan, 




Glasgow. 


Millar, 


8 Wilberforce Street, Wall- 




send-on-Tyne. 


MiUer, 


13 Park Groye Terrace, 




W., Glasgow. 


Milne, 


7 Carmichael Street, Govan. 


Mitchell, 


Glasgow. 


Moir, 


Forth BridgeWorks, South 




Queensferry. 


Moir, 


26 St. Hilda Street, Hartle- 




pool. 


Morch, 


Horten, Norway. 


Morrison, 


8 Annfield Terrace, Partick, 




Glasgow. 


Monro, 


629 Goyan Road, Govan 




Glasgow. 


Murray, 


47 Kelvinhaugh Street, 




Glasgow. 


Napier, 


22 Salisbury PI., HiUhead, 




Glasgow. 


42 





324 Graduates. 

1884, Feb. 26: D. J. NeviD, 352 St. Vincent Street, 

Glasgow. 

1879, Not. 26: Alex. R. Paton, Redthorn,Partick,Glasgow. 

1884, Feb. 26: Matthew Paul, Jun., Levenford Works, Dnm- 

barton^ 
1873, Pec. 23: Edward C. Peck, Yarrow & Co., Poplar, 

London, E. 

1881, Oct. 25: William T. Philp, 284 Bath Street, Glasgow. 

1885, Jan. 27: James L. Prondfoot, 154 West George Street, 

Glasgow. 

1885, Feb. 24: John T. Ramage, The Hawthorn's, Benning- 
ton, Edinburgh. 

1883, Nov. 21: Hugh Reid, 10 Woodside Terrace, 

Glasgow. 

1884, Dec. 23: James G. Reid, jun., 4 Holland Place, Glasgow. 
1884, Feb. 26: Walter Reid, 90 Bellgrove St, Glasgoir. 

1882, Nov. 28: J. M'E. Ross, Ravensleigh, Dowanhill 

Gardens, Glasgow. 
1884, Mar. 25: J. B. Sanderson, 15 India Street, Glasgow. 

1879, Mar. 25: John Scobie, Samana Railway, Samana. 

St. Domingo. 

1880, Apr. 27: Archibald Sharp, 31 Morrison St., Glasgow. 

1882, Oct. 24: John Sharp, 461 St. Vincent St, Glas- 

gow. 

1883, Jan. 23:AdolphTJ. Sheldon, 91 Pollok Street, Gla^ow. 

1883, Dec. 18: George Simpson, 13 Maxwell Street, Partick, 

Glasgow. 
1877, Mar 20: Nisbet Sinclair, jun., 43 Park Road, Glasgow. 

1884, Mar. 25: Russell Sinclair, 49 Stanley St., W. North 

Shields. 

1882, Nov. 28: Geo. H., Slight, jun., 413 East India Road, 

London, E. 

1881, Nov. 22: John A. Steven, 12 Royal Crescent, Glas- 

gow. 



Oraduaies. 



325 



1873, Doe. 23: John 



Stewart, 



1881, Jan. 25: William Steyenson, R. & J. Hawthorn, St. 

Peter's WorkSjNewcastle- 
on-Tyne. 

270 New City Road, Glas- 
gow. 

02 Bothwell Circ, Glasgow. 

1 1 Florence PL, Glasgow. 

Caledonian Railway Work?, 
St. Rollox, Glasgow* 



1875, Dee. 21: Andrew Stirling, 
1884, Dec 23: David W, Stnrrock, 
1878, Jan. 22: Benjamin B. Sykes, 



1880, Dec. 21: Stanley 
1883, Dec. 18: Lewis 

1882, Not. 28: William 

1883, Apr. 24: Wm. R. 
1880, Nov. 23: George 
1874, Feb. 24: George C. Thomson, 

1884, Dec. 23: John 



Tatham, 
Taylor, 
Taylor, 
Taylor, 



2 Cambridge Gate, Regent's 
Park, London, N.W. 

2 Hillsborongh Terrace, 
Hillhead, Glasgow. 

57 St. Vincent Cres., Glas- 
gow. 

Lennox, Lang, & Co., 131 

W. Regent St., Glasgow. 

Thomson, 64 Sycamore Road, Hands- 

worth, near Birmingham. 

39 Eersland Terrace, Hill- 
head, Glasgow. 
Thomson, Jan., 15 Barnbank Gardens, 



Glasgow. 

1883, Dec. 18: Nicol Thomson, 39 Kelvinhaugh Street, 

Glasgow. 

1884, Dec 23: William Thomson, 15 Bombank Gardens, 

Glasgow. 

1885, Feb 24: Charles H, Wannop, 12 Derby Street, Glasgow, 
1884, Feb. 26: William Warrington, 23 Miller Street^ Glasgow. 
1881, Mar, 22: Robert Watson, 1 Glencairn Drive, Pollok- 

shields, Glasgow. 
1880, Apr. 27: Robert D. Watt, Butterfield, Swire, & Co., 

Shanghai. 



836 Gradvaies. 

1875, Dec. 21: Richard G. Webb, 60 Warwick Gardens, Ken- 

sington, London. 
1878, Dec. 17: Robert L. Weighton, M.A., R. & J. Hawthorn, 

St. Peter's, Newcastle. 
on-Tyne. 

1884, Apr. 22: John Weir, Ramage & Fergnson, Ship- 

bnilders, Leith. 

1882, Nov. 28: Geo. B. Wemyss, Glasgow. 

1883, Dec. 18: John Whitehead, 71 Scott Street, Gamethill 

Glasgow. 

1877, Jan. 23: Robt. John Wight, 7 Berlin Place, PoUok- 

shields, Glasgow. 

1879, Oct. 28: William WiUox,M.A., 27 Albert Terrace, Aber- 
deen. 

1883, Jan. 23: John Wilson, 175 North Street, Glasgow. 

1883, Dec. 18: David Wood, 124 West Nile Street, 

Glasgow. 

1885, Mar. 24: Fred. W. Zncker, Dumbarton. 



INDEX. 



PAGE 

Address by the Piesidest, ...... i 

Prosperity of the Institution, ..... i 

Fandamental Principles of the Kinetic Branch of DynatnicH - 2 

Inertia of Matter, ....... 2 

Changing Motion, ....... 3 

Newton's Laws, --.-... 5 

Law of Inertia, ....... 7 

Principle of Chronometry, ----.. 8 

Force Tests Applied to Engineering Structnres, . .12 

Additions to Library, ....... 289 

American Railway Freight Cars— by Mr Alexander Findlay, - - 253 
Bogie Carriages, -.-.-. 254—267 

Wheelsand Axles, &c., ...... 255 

Galvanised Iron Roof Covering, ..... 260 

Approximation to Curves of Stability, from Data for Known Ships— 
by Messrs F. P. Purvis and B. Kindermann^ 

Discussion of Paper, -•---.. 15 

Butt Fastening of Iron Vessels—by Mr Staveley Taylor, 227 

Weakness of Butt Joints, ..... 227 

Double Butt Straps, ....... 229 

Lapped Joints, ....... 230 

Relative Proportions of Rivet Area to Plate Section, - 233 

Discussion, ....... 247—249 

Bridge— Forth, 21 

M Tay, 263 

Bogie Trucks, 254-267 



Continuous Regenerative Gas Kiln for Baming Fire Bricks, Puttery, 
&c.— by Mr John Mayer, F.C.S., - 
Regenerative System of Gas Firing, 
Kiln Firing by Heat Regeneration, - 
Gas Producers, 

Continuous Regenerative Gas Kiln, 
Discussion, .... 



207 
207 
208 
209 
209 
219 



328 Ind$x. 

PAGE 

Chronometry—Principle of, -..-.. g 

Cars—American Railway Freight, 253 

Cylinders for Bridge Foundations, . -263 

Deceased Members, .... • - . :29i- 

Diggers for Excavating in Bridge Pier Cylinders, - *2S: 

Discussion of Papers • 

Remarks by— Mr J. H. Biles— Speed Trials, 177.— Mr Wm. Denny 
— Relations of Speed and Power in Steam Vessels, 178. — ^Mr F. 
W. Dick— Strength of Steel Plates, 32. - Mr W. T. C. Dutton - 
Strength of Rivets, 249, Outside Butt Straps, 250.— Mr Henry 
Dyer— Power and Speed, 161, Regenerative Gas Kiln, 222, 
Outside Butt Straps, 248.— Professor Elgar — Progressive 
Speed Trials and Model Experiments, 173.— Mr J. Macfar- 
lane Gray— Types of Vessels. 18.— Mr Jas. UamOton, Jun.— 
Speed Curves, 159, Wave Formation, 161. — Mr Ebenezer 
Kemp— Chimney Draught, 219. — Mr C. C. Lindsay — Regener 
ative Gas Kiln, 222.— Mr Robert Mansel— Stability of Ships, 
16, Relation of Speed and Power in Steam Vessels, 136, 
Strength of Steam Ships 247. — Mr John Mayer— Regener- 
ative Gas Kiln, 220, 223.— Mr F. P. Purvis— Approximation 
to Curves of Stability, 15, 18.— Mr George Russell— Butt 
Straps, 249. —Professor James Thomson, President— Electrical 
Propulsion, 205, Hoffmann Brick Kiln, 220. — Mr Geoige 
Thomson - Speed Curves, 168, Model Experiments, 169, Wave 
Formation, 169.— Mr Henry H. West— Butt Rivetting, 251. 
Donations to Librar}', --.--.. 289 
Drilling Steel Plates, 28 

Electrical Navigation— by Mr Allan Clark, • . . - 201 

Electric Batteries, -------- 201 

Energy and Entropy and their Applications to the Theories of Air and 

Steam— by Mr Heniy Dyer, C.E,, M.A., - - . . 35 

First Law of Thermo-dynamics, ----- 37 

Second Law of Thermodynamics, - • - - - 3S 

Real Dynamical Specific Heat, - - - - . 43 

Apparent Specific Heat, ------ 43 

General Equation of Thermo-dynamics, ... .43 

Metamorphic Function, -.-... 43 

Air Considered as a Perfect Gas, ----- 45 

Saturated Steam, •----.. 4s 

Superheated Steam, ....... 55 



Index. 

Fire-bricka— Burning of , - 
Formnlie for Power and Speed, - 
Foandations by Cylinders, 
Froade's System of Model Experiments, 

Gas Furnace for Plate Heating, - 
Gas Producers, 

Inertia of Matter, • 

Institution— Prosperity of, 
„ —Papers Head, 
„ —List of Members of the, 
, , — Office-Bearen of the, 

Law of Inertia, - : 

Laws of Motion, 

Laws of Thermo-dynamics, 

Library of the Institution, 

„ —List of Books recently added to, 
„ —List of Donations to, - 

List of Members, - 



Manipulating the Material, and Building and Prilling the Great 

Andrew S. Biggart, C.E., 



&c., 



Tubes of the Forth Bridge— by Mr 

Dimensions of Struts, 

Gas Furnace for Heating Plates, 

Hydraulic Bending Press, 

Annealing of Steel Plates, - 

Building and Drilling of the Tul>es, 

Discussion, 
Members— List of, - 
Minutes of Proceedings, - 
Model Experiments, 
Mr Mansel's and the late Mr Froude 

Results of Progressive Speed Trials— by Mr William Denny, 

Analyses of Progressive Trial Results, 



829 

PAGE 
207 
140 
263 
133 

23 

209 

2 

1 

1 

293 

iii. 

7,9 
5 

37 
291 
289 
289 
293 



21 

22 

23 

23,25 

24 

26,29 

82 

293 

273 

79, 85, 90, 188. 141, 175 

s Methods of Analysing the 

65 
68 



Analyses of Indicated Horse-Power, 
Discussion, - - . . 



90 
100, 186, 161 



New Books Added to Library, . - - - - - 289 

Note on Tests of Turbines— by Professor R. H. Thurston, C.E., &c., - 199 



Offico-Bearers, 



830 Index 

PAGE 

Papers Kead, — 

PresidenfB Address, ...... .1 

Approximation to Curves of Stability (Discussion), - 15 

Building and Drilling Tubes of Forth Bridge,- • - II 
Energy and Entropy, and their Application to the Theories of Air 

and Steam, ....... - 35 

.Mr Mansers and the late Mr Fronde's Methods of Analysing the 

Kesults of Progressive Speed Trials, ... .63 

Note on Tests of Turbines, . - . . - - 199 

Electrical Navigation, ..... .201 

Continuous Regenerative Gas Kiln for Burning Fire-bricks« 

Pottery, &c., - • - - - - - 207 

Butt Fastenings of Iron Vessels, .... • 227 

American Railway Freight Cars, .... - SSI 

Sinking the Cylinders of the Tay Bridge by Pontoons, - - 263 

Periodicals Received at Library, - . - • - - S90 

Pontoons for Sinking Cylinders, . . . . • - 264 

Portrait Album, ....... - 290 

Power— Expenditure of Indicated Horse, • 84—90 

Power and Speed Formula?, ..... - 140 

President's Address, ...... .1 

Progressive Speed Trials of Steam Vessels, ... .66 

Regenerative Gas Kiln, ..--.- .207 

Rivetting— Strength of, - - - - . - 2M 

Railway Freight Cars— American, • - - 253 

Saturated Steam, .-.-.-.. 48 
Second Law of Thermo-dynamics, • • - • - 38 

Shearing Strength of Steel and Iron Rivets, . - . 236, 249 

Sinking the Cylinders of the Tay Bridge by Pontoons— by Mr Andrew 

S. Biggart, C.E., 263 

Foundations by Cylinders, ...... 963 

Pontoons for Sinking Cylinders, - - - - 264 

Hydraulic Machinery, •••••• 265 

Specific Heat, ----..-. 43 

Speed and Power in Steam Vessels, - 65, 163 

Stability of Ships, -•--•■-. 15 
Strength of Structures, ....... n 

„ of Steel Plates, 24, 32 

„ of Butt Joints, -•-■•-. 228 
Superheated Steam, •--•'.. 55 



Index. 

TaUes of- 

Pressures, Yolnmes, Ac, of Superheated Steam, - 
M of Dry Saturated Steam, 

Initial Friction in Marine Engines, • 

Analyses of Indicated Horse-Power, - 

Elements of the Distribution of Power in Paddle Steamers, 

Speed— Resistance, ..... 

Rivet Area and Plate Section, 

Sheariog Tests of Plate Joints. 
T»y Bridge, ...... 

Tests of Strength, ...... 

Theorem of Newton on Similarity of Motion— F. Rdech, 
Thermo-dynamics, ...... 

Treaaurer's Statement^ ..... 

Turbines— Tests of, ..... 



881 

PAQS 

59 
60,62 
97 
•98,99 
101 
147, 150 
239—243 
244 
263 
12 
190 



284 
199 



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